Tomoyuki Shirai | Last modified date：2016.08.19 |

Graduate School

Undergraduate School

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 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, 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. |

Educational

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