Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1214/17-AAP1371

Language：English   Publishing type：Research paper (scientific journal)  

This paper studies a higher dimensional generalization of Frieze's ζ(3) -limit theorem on the d-Linial–Meshulam process. First, we define spanning acycles as a higher dimensional analogue of spanning trees, and connect its minimum weight to persistent homology. Then, our main result shows that the expected weight of the minimum spanning acycle behaves in Θ (n^{d-1}).

DOI： 10.1002/rsa.20718

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.3792/pjaa.93.1

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1214/ECP.v20-4252

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s00440-015-0644-6

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.2969/jmsj/06720763

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/S0022-1236(03)00171-X

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1214/aop/1055425789

Publisher：Leibniz International Proceedings in Informatics, LIPIcs  

It is celebrated that a simple random walk on ℤ and ℤ2 returns to the initial vertex v infinitely many times during infinitely many transitions, which is said recurrent, while it returns to v only finite times on ℤd for d ≥ 3, which is said transient. It is also known that a simple random walk on a growing region on ℤd can be recurrent depending on growing speed for any fixed d. This paper shows that a simple random walk on {0, 1, ⋯, N}n with an increasing n and a fixed N can be recurrent depending on the increasing speed of n. Precisely, we are concerned with a specific model of a random walk on a growing graph (RWoGG) and show a phase transition between the recurrence and transience of the random walk regarding the growth speed of the graph. For the proof, we develop a pausing coupling argument introducing the notion of weakly less homesick as graph growing (weakly LHaGG).

DOI： 10.4230/LIPIcs.AofA.2024.22

Scopus

Publisher：Leibniz International Proceedings in Informatics, LIPIcs  

It is a celebrated fact that a simple random walk on an infinite k-ary tree for k ≥ 2 returns to the initial vertex at most finitely many times during infinitely many transitions; it is called transient. This work points out the fact that a simple random walk on an infinitely growing k-ary tree can return to the initial vertex infinitely many times, it is called recurrent, depending on the growing speed of the tree. Precisely, this paper is concerned with a simple specific model of a random walk on a growing graph (RWoGG), and shows a phase transition between the recurrence and transience of the random walk regarding the growing speed of the graph. To prove the phase transition, we develop a coupling argument, introducing the notion of less homesick as graph growing (LHaGG). We also show some other examples, including a random walk on {0, 1}n with infinitely growing n, of the phase transition between the recurrence and transience. We remark that some graphs concerned in this paper have infinitely growing degrees.

DOI： 10.4230/LIPIcs.SAND.2024.17

Scopus

Publisher：Journal of Applied and Computational Topology  

We compute the eigenvalues of up-Laplacians on cubical lattices and derive the torsion-weighted count of spanning acycles in cubical lattices by using the matrix-tree theorem for simplicial/cell complexes. As a corollary, we show that the torsion-weighted spanning acycle entropy of a cubical lattice defined on Zb×∏j=b+1q{0,1,⋯,nj} is expressed as a linear combination of logarithmic Mahler measures.

DOI： 10.1007/s41468-024-00163-y

Scopus

Publishing type：Research paper (scientific journal)  

We are concerned with zeros of random power series with coefficients being a stationary, centered, complex Gaussian process. We show that the expected number of zeros in every smooth domain in the disk of convergence is less than that of the hyperbolic Gaussian analytic function with i.i.d. coefficients. When coefficients are finitely dependent, i.e., the spectral density is a trigonometric polynomial, we derive precise asymptotics of the expected number of zeros inside the disk of radius r centered at the origin as r tends to the radius of convergence, in the proof of which we clarify that the negative contribution to the number of zeros stems from the zeros of the spectral density.

DOI： 10.1007/s10959-022-01203-y

Web of Science

Scopus

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.7566/JPSCP.40.011

Publisher：Modern Stochastics: Theory and Applications  

Random filtered complexes built over marked point processes on Euclidean spaces are considered. Examples of these filtered complexes include a filtration of Čech complexes of a family of sets with various sizes, growths, and shapes. The law of large numbers for persistence diagrams is established as the size of the convex window observing a marked point process tends to infinity.

DOI： 10.15559/22-VMSTA214

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Japan Academy  

We consider the Laplace-Beltrami operator $\Delta_g$ on
a smooth, compact Riemannian manifold $(M,g)$
and the determinantal point process $\xila$ on $M$ associated with the spectral
projection of $-\Delta_g$ onto the subspace corresponding to the eigenvalues up to
$\la^2$.
We show that the pull-back of $\xila$ by the exponential map
$\exp_p : T_p^*M \to M$ under a suitable scaling converges
weakly to the universal determinantal point process on
$T_p^* M$ as $\la \to \infty$.

DOI： 10.3792/pjaa.98.018

Web of Science

Scopus

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.1007/s10959-022-01203-y

Language：English   Publishing type：Research paper (scientific journal)  

DOI： DOI 10.15559/22-VMSTA214

Publisher：Institute of Electrical and Electronics Engineers ({IEEE})  

Disordered complex networks are of fundamental interest as stochastic models
for information transmission over wireless networks. Well-known networks based
on the Poisson point process model have limitations vis-a-vis network
efficiency, whereas strongly correlated alternatives, such as those based on
random matrix spectra (RMT), have tractability and robustness issues. In this
work, we demonstrate that network models based on random perturbations of
Euclidean lattices interpolate between Poisson and rigidly structured networks,
and allow us to achieve the best of both worlds : significantly improve upon
the Poisson model in terms of network efficacy measured by the Signal to
Interference plus Noise Ratio (abbrv. SINR) and the related concept of coverage
probabilities, at the same time retaining a considerable measure of
mathematical and computational simplicity and robustness to erasure and noise.
We investigate the optimal choice of the base lattice in this model,
connecting it to the celebrated problem optimality of Euclidean lattices with
respect to the Epstein Zeta function, which is in turn related to notions of
lattice energy. This leads us to the choice of the triangular lattice in 2D and
face centered cubic lattice in 3D. We demonstrate that the coverage probability
decreases with increasing strength of perturbation, eventually converging to
that of the Poisson network. In the regime of low disorder, we approximately
characterize the statistical law of the coverage function.
In 2D, we determine the disorder strength at which the PTL and the RMT
networks are the closest measured by comparing their network topologies via a
comparison of their Persistence Diagrams . We demonstrate that the PTL network
at this disorder strength can be taken to be an effective substitute for the
RMT network model, while at the same time offering the advantages of greater
tractability.

DOI： 10.1109/TIT.2022.3163604

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/2009.08811v1

Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures [Formula: see text] on a space S with measure [Formula: see text], whose correlation functions are all given by determinants specified by an integral kernel K called the correlation kernel. We consider a pair of Hilbert spaces, [Formula: see text], which are assumed to be realized as [Formula: see text]-spaces, [Formula: see text], [Formula: see text], and introduce a bounded linear operator [Formula: see text] and its adjoint [Formula: see text]. We show that if [Formula: see text] is a partial isometry of locally Hilbert–Schmidt class, then we have a unique DPP [Formula: see text] associated with [Formula: see text]. In addition, if [Formula: see text] is also of locally Hilbert–Schmidt class, then we have a unique pair of DPPs, [Formula: see text], [Formula: see text]. We also give a practical framework which makes [Formula: see text] and [Formula: see text] satisfy the above conditions. Our framework to construct pairs of DPPs implies useful duality relations between DPPs making pairs. For a correlation kernel of a given DPP our formula can provide plural different expressions, which reveal different aspects of the DPP. In order to demonstrate these advantages of our framework as well as to show that the class of DPPs obtained by this method is large enough to study universal structures in a variety of DPPs, we report plenty of examples of DPPs in one-, two- and higher-dimensional spaces S, where several types of weak convergence from finite DPPs to infinite DPPs are given. One-parameter ([Formula: see text]) series of infinite DPPs on [Formula: see text] and [Formula: see text] are discussed, which we call the Euclidean and the Heisenberg families of DPPs, respectively, following the terminologies of Zelditch.

DOI： 10.1142/S2010326322500253

Web of Science

Scopus

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Publishing type：Research paper (scientific journal)  

The article [Absolute continuity and singularity of Palm measures of the Ginibre point process], written by [Hirofumi Osada and Tomoyuki Shirai], was originally published Online First without Open Access. After publication in volume [165], issue [3–4], page [725–770] the author decided to opt for Open Choice and to make the article an Open Access publication. Therefore, the copyright of the article has been changed to © [The Author(s)] [2021] and this article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. Ifmaterial is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The original article has been corrected.

DOI： 10.1007/s00440-021-01094-w

Web of Science

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On an annulus ${\mathbb{A } }_q :=\{z \in {\mathbb{C } }: q < |z| < 1\}$ with a
fixed $q \in (0, 1)$, we study a Gaussian analytic function (GAF) and its zero
set which defines a point process on ${\mathbb{A } }_q$ called the zero-point
process of the GAF. The GAF is defined by the i.i.d. Gaussian Laurent series
such that the covariance kernel parameterized by $r >0$ is given by the
weighted Szeg\H{o} kernel of ${\mathbb{A } }_q$ with the weight parameter $r$
studied by Mccullough and Shen. The GAF and the zero-point process have
symmetry associated with the $q$-inversion of coordinate $z \leftrightarrow
q/z$ and the parameter change $r \leftrightarrow q^2/r$, and when $r=q$ they
are invariant under conformal transformations which preserve ${\mathbb{A } }_q$.
Conditioning the GAF by giving zeros, new GAFs are induced such that the
covariance kernels are also given by the weighted Szeg\H{o} kernel of
Mccullough and Shen but the weight parameter $r$ is changed depending on the
given zeros. Then we prove that the zero-point process of the GAF provides a
permanental-determinantal point process (PDPP) in which each correlation
function is expressed by a permanent multiplied by a determinant. Dependence on
$r$ of the unfolded 2-correlation function of the PDPP is studied. If we take
the limit $q \to 0$, a simpler but still non-trivial PDPP is obtained on a
punctured unit disk ${\mathbb{D } }^{\times} := {\mathbb{D } } \setminus \{0\}$. In
the further limit $r \to 0$ the present PDPP is reduced to the determinantal
point process on ${\mathbb{D } }$ studied by Peres and Vir\'ag.

DOI： 10.1007/s00220-022-04365-2

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/2008.04177v1

Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.1088/1751-8121/abecaa

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Other Link： http://hdl.handle.net/2433/260647

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.13044/j.sdewes.d6.0221

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.7494/OpMath.2019.39.3.361

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1029/2017WR021864

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.19195/0208-4147.37.2.12

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.indag.2016.02.003

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1587/transcom.2016NEI0001

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1239/aap/1409319562

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1214/EJP.v18-2545

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.3792/pjaa.86.33

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.2206/kyushujm.62.281

Language：English   Publishing type：Research paper (other academic)  

Language：English   Publishing type：Research paper (scientific journal)  

We give a probabilistic expression of the α-determinant by using the Wishart distribution on the cone of positive definite matrices. As a corollary, we give a partial answer to a positivity problem for the α-determinant which is equivalent to the existence problem of certain multivariate probability distributions. We also give a concrete example to support our conjecture for the positivity.

DOI： 10.2206/kyushujm.61.169

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s11118-006-9027-z

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s10955-006-9026-x

Language：English   Publishing type：Research paper (international conference proceedings)  

Language：English   Publishing type：Research paper (other academic)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.2748/tmj/1113246940

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1017/S0027763000008412

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1017/S0027763000022157

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.2969/jmsj/05210099

Language：English   Publishing type：Research paper (scientific journal)  

For discrete magnetic Schrödinger operators on covering graphs of a finite graph, we investigate two spectral properties: (1) the relationship between the spectrum of the operator on the covering graph and that on a finite graph, (2) the analyticity of the bottom of the spectrum with respect to magnetic flow. Also we compute the second derivative of the bottom of the spectrum and represent it in terms of geometry of a graph.

DOI： 10.1006/jfan.1999.3478

Language：English   Publishing type：Research paper (other academic)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1006/jfan.1998.3322

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

We discuss two types of trace formula which arise from the inverse spectral problem for discrete Schrödinger operators as L = -Δ + V (x) where V is a bounded potential. One is the relationship between a potential and spectral data, and another is the one between the green function of L and periodic orbits of a state space.

DOI： 10.2977/prims/1195144826

Total pages：xi, 258 p.   Language：English  

CiNii Books

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Event date： 2015.2

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2014.11

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2014.9

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2012.6

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：理化学研究所   Country：Japan  

Event date： 2011.12

Presentation type：Oral presentation (invited, special)  

Country：Japan  

Event date： 2011.12

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2010.12

Presentation type：Oral presentation (general)  

Country：Japan  

Random analytic functions and their zeros

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：九州大学伊都キャンパス   Country：Japan  

Event date： 2024.7

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Chuo University   Country：Japan  

Other Link： https://sites.google.com/g.chuo-u.ac.jp/event-website/home

Event date： 2024.3

Language：English   Presentation type：Oral presentation (general)  

Country：Netherlands  

Event date： 2024.3

Language：English   Presentation type：Oral presentation (general)  

Country：France  

Event date： 2023.12

Language：English   Presentation type：Oral presentation (general)  

Country：Singapore  

Event date： 2023.10

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.8

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.3

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Event date： 2022.12

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.12

Language：English   Presentation type：Oral presentation (invited, special)  

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Event date： 2022.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Tohoku University, Sendai.   Country：Japan  

Event date： 2022.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.11

Language：English   Presentation type：Oral presentation (invited, special)  

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Event date： 2022.8 - 2022.9

Language：English   Presentation type：Oral presentation (invited, special)  

Country：Singapore  

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Event date： 2022.8

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.8

Language：English   Presentation type：Oral presentation (invited, special)  

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Event date： 2022.6

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：中央大学   Country：Japan  

Event date： 2022.6

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.6

Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Event date： 2022.1

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：統計数理研究所.   Country：Japan  

Event date： 2021.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：オンライン   Country：Japan  

Event date： 2021.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2020.6

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2020.6

Language：English   Presentation type：Oral presentation (general)  

Country：Sweden  

Event date： 2019.5

Language：English   Presentation type：Oral presentation (general)  

Country：Korea, Republic of  

Event date： 2019.4

Language：Japanese  

Country：Japan  

Event date： 2019.4

Language：English   Presentation type：Oral presentation (general)  

Country：Morocco  

Event date： 2018.6 - 2020.6

Language：English   Presentation type：Oral presentation (general)  

Country：Singapore  

Event date： 2018.2

Language：English  

Country：United States  

Event date： 2017.9

Language：English   Presentation type：Oral presentation (general)  

Country：Germany  

Event date： 2017.8

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2016.5

Language：English  

Country：United States  

Event date： 2015.5

Language：English  

Country：India  

Event date： 2014.8

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2014.7

Language：English  

Country：Canada  

Event date： 2014.5

Language：English  

Venue：Hammamet   Country：Tunisia  

Coverage probability is one of the most important metrics for evaluating the performance of wireless networks. However, the spatial stochastic models for which a computable expression of the coverage probability is available are restricted (such as the Poisson based or α-Ginibre based models). Furthermore, even if it is available, the practical numerical computation may be time-consuming (in the case of α-Ginibre based model). In this paper, we propose the application of Padé approximation to the coverage probability in the wireless network models based on general spatial stationary point processes. The required Maclaurin coefficients are expressed in terms of the moment measures of the point process, so that the approximants are expected to be available for a broader class of point processes. Through some numerical experiments for the cellular network model, we demonstrate that the Padé approximation is effectively applicable for evaluating the coverage probability.

Event date： 2013.3

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Country：Japan  

Event date： 2013.1

Language：English  

Country：Japan  

Event date： 2012.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：京都大数理解析研究所   Country：Japan  

Event date： 2012.8

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：小山高専   Country：Japan  

Event date： 2012.3

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.12

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.11

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.10

Presentation type：Oral presentation (general)  

Venue：奈良女子大学   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：IBM Tokyo   Country：Japan  

Event date： 2011.9

Presentation type：Oral presentation (general)  

Venue：IBM Tokyo   Country：Japan  

Event date： 2011.6

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.3

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.2

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2011.1

Presentation type：Oral presentation (general)  

Venue：Komaba Campus, The University of Tokyo   Country：Japan  

Event date： 2011.1

Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2009.1

Presentation type：Oral presentation (general)  

Country：Korea, Republic of  

Event date： 2009.1

Presentation type：Oral presentation (general)  

Country：Korea, Republic of  

Event date： 2008.10

Presentation type：Oral presentation (general)  

Country：Japan  

Presentation type：Oral presentation (general)  

Country：Japan  

Other Link： http://www2.math.kyushu-u.ac.jp/~shirai/numprob2007/index.html

Presentation type：Oral presentation (general)  

Country：Japan  

Presentation type：Oral presentation (general)  

Country：Italy  

Presentation type：Oral presentation (general)  

Country：Poland  

Presentation type：Oral presentation (general)  

Country：United States  

Presentation type：Oral presentation (general)  

Country：United States  

Presentation type：Oral presentation (general)  

Country：Japan  

Other Link： http://stokhos.shinshu-u.ac.jp/salsis2007/index.html

Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese   Publishing type：Book review, literature introduction, etc.  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

The non-commutative harmonic oscillators (NcHO) and 2p-quantum Rabi models
(2pQRM) are extensions of harmonic oscillators. The purpose of this paper is to
give a relationship between NcHO and 2pQRM, and the fiber decomposition of NcHO
by 2pQRM is shown. We also construct Feynman-Kac formulas of NcHO and 2pQRM.
Then asymptotic behaviors of the spectral zeta function of 2pQRM is considered.

arXiv

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Other Link： http://arxiv.org/pdf/2408.04239v2

The renormalized spectral zeta function of the quantum Rabi Hamiltonian is
considered. It is shown that the renormalized spectral zeta function converges
to the Riemann zeta function as the coupling constant goes to infinity.
Moreover the path measure associated with the ground state of the quantum Rabi
Hamiltonian is constructed on a discontinuous path space, and several
applications are shown.

arXiv

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Other Link： http://arxiv.org/pdf/2405.09158v2

We obtain first order linear partial differential equations which are
satisfied by exponential generating functions of two variables for the number
of connected bipartite graphs with given Betti number. By solving these
equations inductively, we obtain the explicit form of generating functions and
derive the asymptotic behavior of their coefficients. We also introduce a
family of basic graphs to classify connected bipartite graphs and give another
expression of the generating functions as the sum over basic graphs of rational
functions of those for the number of labeled bipartite rooted spanning trees.

arXiv

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Other Link： http://arxiv.org/pdf/2208.03996v2

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：2

Type：Scientific advice/Review 

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：2

Type：Academic society, research group, etc. 

Type：Scientific advice/Review 

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：9

Type：Academic society, research group, etc. 

Type：Competition, symposium, etc. 

Number of participants：150