Hirofumi Osada | Last modified date：2015.12.9 |

Graduate School

Undergraduate School

E-Mail

Homepage

##### http://www2.math.kyushu-u.ac.jp/~osada/public-2_html/index.html

This is a home page of the grant "Stochastic geometry and stochastic dynamics of infinite particle systems interacting through 2 dimensional Coulomb potentials" .

##### http://www2.math.kyushu-u.ac.jp/~osada/public-2_html/index.html

This is a home page of the grant "Infinite-dimensional stochastic dynamical system related to Random matrices and statistical physics" .

Academic Degree

the degree of Doctor of Science

Field of Specialization

Probability Theory

Outline Activities

My main subject is the probability theory. I study in particular that various mathmatical problems arising from statistial physics. I organized a symposium concerning on these and make this research field active. In our department, we have a regular seminar on probability theory. We invite various people to our seminar. This is a good opportunity for our study.

Research

**Research Interests**

- Probability Theory

keyword : Probability Theory, Stochastic Analysis, Homogenization of diffusions, diffusions on fractals, infinite particle systems, interacting Brownian motions, Random Matrices

1980.04.

**Academic Activities**

**Papers**

1. | Hirofumi Osada, Hideki Tanemura,Strong Markov property of determinantal processes with extended kernels.,Stochastic Processes and their Applications,Vol.126,2016.01. |

2. | Hirofumi Osada, Tomoyuki Shirai,Absolutely continuity and singularity of Palm measures of the Ginibre point process,Probability Theory and Related Fields,published on line (46 pages),2015.07. |

3. | Hirofumi Osada,Interacting Brownian motions in infinite dimensions with logarithmic interaction potentialsII: Airy random point field.,Stochastic Processes and their Applications,Vol.123,No.3,2013.03. |

4. | Hirofumi Osada,Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials,Annals of Probability,Vol.４１,2013.01. |

5. | Hirofumi Osada,Infinite-dimensional stochastic differential equations related to random matrices,Probability theory and related fields,Vol.153 ,No.no. 3-4,pp.471–509,2012.03. |

6. | Hirofumi Osada,Tagged particle processes and their non-explosion criteria,Journal of the mathematical society of Japan,Vol.62,No.3,pp.867-894,2010.06. |

**Awards**

- Itô Prize 2013 Hirofumi Osada

"Interacting Brownian motions in infinite dimensions with logarithmic

interaction potentials II: Airy random point field" SPA 123 (2013), 813-838.

This is one of a series of papers by Hirofumi Osada on infinite systems of

interacting particles with logarithmic interaction potentials.

Osada’s problem concerns the construction of the natural diffusion

process associated with certain systems of infinite dimensional

interacting particles by Dirichlet form techniques. For short range

potentials there are well-known results, but Osada considers a

logarithmic interaction potential, where none of the previously existing

theories applies. In particular, the potential is not of Ruelle type and the

equilibrium state is no longer a Gibbs measure.

In this series of papers, Osada introduces the notion of quasi-Gibbs

property, and uses the logarithmic derivative and the scaling property of

the potential to construct the diffusion process for the particle system. The

corresponding infinite dimensional SDE is solved as well. Of particular

importance are the cases of Dyson's Brownian motion and the Ginibre

point process, both studied by Osada in the previous parts of the series.

In this paper, Osada shows how his machinery can be applied to the

Airy random point field, by giving a new sufficient condition for the

quasi-Gibbs property. Note that the Airy field arises very naturally as the

edge behavior of Dyson's Brownian motion and it has a close connection

to random matrix theory. Due to the spatial inhomogeneity, the Airy field

presents additional difficulties. It is very impressive that the construction

of the diffusion is still possible for this field.

This work of Osada makes a bridge between fundamental breakthroughs

concerning infinite systems of interacting particles and random matrix

theory. It provides important new classes of stochastic processes with

values in the configuration space. For these reasons, the board of the

SPA journal decides to award the Itô Prize 2013 to this paper.

Educational

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