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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
Educational Activities
In addition to the lectures on the general education, and engineering, and the mathematical science, I am a superviser of sutudents in docter course and master course. I am also concerned with a seminar class of the 3th grade.