|Hirofumi Osada||Last modified date：2016.10.20|
This is a home page of the grant "Stochastic geometry and stochastic dynamics of infinite particle systems interacting through 2 dimensional Coulomb potentials" .
This is a home page of the grant "Infinite-dimensional stochastic dynamical system related to Random matrices and statistical physics" .
the degree of Doctor of Science
Field of Specialization
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.
- Probability Theory
keyword : Probability Theory, Stochastic Analysis, Homogenization of diffusions, diffusions on fractals, infinite particle systems, interacting Brownian motions, Random Matrices
1980.04I study diffusions on singular spaces. Typical examples of singular spaces are infinitely many particle systems that are appeared in statistical physcis and fractals. These spaces are quite interesting; nevertheless, it is difficult to study diffusions on these spaces because of the usual method cannot be applied to these spaces..
|1.||Hirofumi Osada, Hideki Tanemura, Strong Markov property of determinantal processes with extended kernels., Stochastic Processes and their Applications, 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, 123, 3, 2013.03.|
|4.||Hirofumi Osada, Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials, Annals of Probability, ４１, 2013.01.|
|5.||Hirofumi Osada, Infinite-dimensional stochastic differential equations related to random matrices, Probability theory and related fields, 153 , no. 3-4, 471–509, 2012.03.|
|6.||Hirofumi Osada, Tagged particle processes and their non-explosion criteria, Journal of the mathematical society of Japan, 62, 3, 867-894, 2010.06.|
- Stochastic Dynamics and Geometry of infinite-particle systems
- 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.