Tomoyuki Shirai | Last modified date：2015.5.19 |

Graduate School

Undergraduate School

E-Mail

Homepage

##### [URL].

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

**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**

1. | 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. |

2. | 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. |

3. | 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. |

4. | Random analytic functions and their zeros,[URL]. |

Educational

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