|Tomoyuki Shirai||Last modified date：2012.5.30|
Ph.D (mathematical science)
Field of Specialization
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.
- Determinantal probability
keyword : determinantal point processes
|1.||Tomoyuki Shirai,Limit theorem for random analytic functions and their zeros,RIMS Kôkyûroku Bessatsu,to appear,2012.07.|
|2.||Takuya Ohwa, Yusuke Higuchi and Tomoyuki Shirai,Exact computation for the cover times of certain classes of trees,Journal of Math-for-Industry,Vol.2,No.A,pp.93-98,2010.04.|
,A remark on monotonicity for the Glauber dynamics on finite graphs,Proceedings of Japan Academy,Vol.86,pp.33-37,2010.01.
|4.||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.|
|5.||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.|
|6.||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.|
|7.||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.||Random analytic functions and their zeros.|