Tomoyuki Shirai | Last modified date：2019.06.24 |

Graduate School

Undergraduate School

Other Organization

Administration Post

Other

E-Mail

Homepage

##### http://imi.kyushu-u.ac.jp/~shirai/

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 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

**Research Interests**

- Persistent homology of random simplicial complexes

keyword : Persistent homology, random simplicial complexes

2013.04. - Determinantal probability

keyword : determinantal point processes

2009.09～2013.09.

**Academic Activities**

**Books**

1. | 白井 朋之, Finite Markov Chains and Markov Decision Processes, Springer Verlag, 5, 189--206, 2014.07. |

**Papers**

**Presentations**

Educational

**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.

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.

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