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Tomoyuki Shirai Last modified date:2022.04.25

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Academic Degree
Ph.D (mathematical science)
Country of degree conferring institution (Overseas)
Field of Specialization
probability theory
Total Priod of education and research career in the foreign country
Outline Activities
It is known that the eigenvalues of a random matrix called Gaussian unitary ensemble have fermionic nature as a random point field. We abstract it and construct a class of random point fields called deteminantal point processes or fermion random fields. The representation of infinite dimensional symmetric group or the zeros of a certain random power series can be expressed as an example. I am now studying its further generalization. There are intimate connections between random walks on graphs, spectra of Laplacians on graphs and the geometric properties of graphs, which I am interested in and would like to clarify. Recently, I am also working on random topology.
Research Interests
  • Persistent homology of random simplicial complexes
    keyword : Persistent homology, random simplicial complexes
  • Determinantal probability
    keyword : determinantal point processes
Academic Activities
1. 白井 朋之, Finite Markov Chains and Markov Decision Processes, Springer Verlag, 5, 189--206, 2014.07.
1. Yasuaki Hiraoka, Tomoyuki Shirai, Khanh Duy Trinh, Limit theorems for persistence diagrams, Annals of Applied Probability, 10.1214/17-AAP1371, 28, 5, 2740-2780, 2018.10, The persistent homology of a stationary point process on RN is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops, cavities, etc. in a multiscale way. The key ingredient is the persistence diagram, which is an expression of the persistent homology. We prove the strong law of large numbers for persistence diagrams as the window size tends to infinity and give a sufficient condition for the support of the limiting persistence diagram to coincide with the geometrically realizable region. We also discuss a central limit theorem for persistent Betti numbers..
2. Yasuaki Hiraoka, Tomoyuki Shirai, Minimum spanning acycle and lifetime of persistent homology in the Linial–Meshulam process, Random Structures and Algorithms, 10.1002/rsa.20718, 51, 2, 315-340, 2017.09, 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})..
3. Alexander Igorevich Bufetov, Tomoyuki Shirai, Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces, Proceedings of the Japan Academy Series A: Mathematical Sciences, 10.3792/pjaa.93.1, 93, 1, 1-5, 2017.01, In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the group of diffeomorphisms of the line with compact support..
4. Tomoyuki Shirai, Trinh Khanh Duy, The mean spectral measures of random Jacobi matrices related Gaussian beta ensembles, Electoric Communications of Probability, 10.1214/ECP.v20-4252, 20, 68, 1-13, 2015.10.
5. Tomoyuki Shirai, Hirofumi Osada, Absolute continuity and singularity of Palm measures of the Ginibre point process, Probability Theory and Related Fields, 10.1007/s00440-015-0644-6, 20, 68, 725-770, 2015.07.
6. Tomoyuki Shirai, Ginibre-type point processes and their asymptotic behavior, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 10.2969/jmsj/06720763, 67, 2, 763-787, 2015.04.
7. Tomoyuki Shirai, Limit theorem for random analytic functions and their zeros, RIMS Kôkyûroku Bessatsu, to appear, 2012.07.
8. Takuya Ohwa, Yusuke Higuchi and Tomoyuki Shirai, Exact computation for the cover times of certain classes of trees, Journal of Math-for-Industry, 2, A, 93-98, 2010.04.
9. Tomoyuki Shirai, Yoichiro Takahashi, Random point fields associted with certain Fredholm determinants (II): fermion shifts and their ergodic properties, Annals of probability, Vol.31, 1533--1564, 2003.01.
10. Tomoyuki Shirai, Yoichiro Takahashi, Random point fields associted with certain Fredholm determinants (I): fermion, Poisson and boson point processes, Journal of Functional Analysis, Vol. 205, 414--463, 2003.01.
1. Tomoyuki Shirai, Determinantal point processes associated with extended kernels and spanning trees on series-parallel graphs, Function theory and dynamics of point processes, 2017.06.
2. 白井 朋之, Probabilistic apsects of persistent homology, La Trobe-Kyushu Joint Seminar on Mathematics for Industry, 2016.06.
3. 白井 朋之, Persistent homology and minimum spanning acycle for certain random complexes, Workshop on "High-Dimensional Expanders 2016", 2016.06.
4. 白井 朋之, Lifetime Sum of Persistent Homology and Minimum Spanning Acycles in Random Simplicial Complexes, Topological Data Analysis on Materials Science, 2015.02.
5. 白井 朋之, Persistent homology of certain random simplicial complexes, 13thSALSIS The 13th workshop on "Stochastic Analysis on Large Scale Interacting Systems", 2014.11.
6. 白井 朋之, Absolute continuity and singularity for the Ginibre point process and its Palm measures, UK-Japan Stochastic Analysis School , 2014.09.
7. Random analytic functions and their zeros.
Educational Activities
I teach probability theory for undergraduate and graduate students,
and applied probability and differential equations for engeering students.
I advise three doctor course students, two master course students and also three undergraduate student at their seminar.
Other Educational Activities
  • 2016.12.
  • 2018.01.