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Tomoyuki Shirai Last modified date:2016.08.19

Graduate School
Undergraduate School

Academic Degree
Ph.D (mathematical science)
Field of Specialization
probability theory
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 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.
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. Tomoyuki Shirai, Ginibre-type point processes and their asymptotic behavior, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 67, 2, 763-787, 2015.04.
2. Tomoyuki Shirai, Evgeny Verbitskiy, Solvable and algebraic systems on infinite ladder , Indagationes Mathematicae, 2016.03.
3. Tomoyuki Shirai, Trinh Khanh Duy, The mean spectral measures of random Jacobi matrices related Gaussian beta ensembles, Electoric Communications of Probability, 20, 68, 2015.10.
4. Tomoyuki Shirai, Hirofumi Osada, Absolute continuity and singularity of Palm measures of the Ginibre point process, Probability Theory and Related Fields, 20, 68, 2015.07.
5. Tomoyuki Shirai, Naoto Miyoshi, A cellular network model with Ginibre configurated base stations, Advances in Applied Probability, To appear, 2013.10.
6. Tomoyuki Shirai, Sho Matsumoto, Correlation functions for zeros of a Gaussian power series and Pfaffians, Electronic Journal of Probability, 18, no. 49, 2013.04.
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 , A remark on monotonicity for the Glauber dynamics on finite graphs, Proceedings of Japan Academy, 86, 33-37, 2010.01.
10. Takuya Ohwa and Tomoyuki Shirai, Joint distribution of the cover time and the last visited point of finite Markov chains, Kyushu Journal of Mathematics, 62, 281--292, 2008.05.
11. 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.
12. 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.
13. Tomoyuki Shirai, Motoko Kotani, Toshikazu Sunada, Asymptotic behavior of the transition probability of a random walk on an infinite graph, Journal of Functional Analysis, Vol.159, 664-689, 1998.01.
1. 白井 朋之, Probabilistic apsects of persistent homology, La Trobe-Kyushu Joint Seminar on Mathematics for Industry, 2016.06.07.
2. 白井 朋之, Persistent homology and minimum spanning acycle for certain random complexes, Workshop on "High-Dimensional Expanders 2016", 2016.06.23.
3. 白井 朋之, Lifetime Sum of Persistent Homology and Minimum Spanning Acycles in Random Simplicial Complexes, Topological Data Analysis on Materials Science, 2015.02.20.
4. 白井 朋之, Persistent homology of certain random simplicial complexes, 13thSALSIS The 13th workshop on "Stochastic Analysis on Large Scale Interacting Systems", 2014.11.06.
5. 白井 朋之, Absolute continuity and singularity for the Ginibre point process and its Palm measures, UK-Japan Stochastic Analysis School , 2014.09.04.
6. Random analytic functions and their zeros.