中央大 統計力学・確率論セミナー

中央大 統計力学・確率論セミナー

講演者：Piotr Graczyk 氏（LAREMA, Universite d'Angers, France）

題　目：Generalized Squared Bessel Matrix Processes and Particle Systems

-- Their Applications in Harmonic Analysis

日　時：２０１６年４月８日（金） １６：００〜１７：３０

場　所：中央大学後楽園キャンパス 理工３号館５階３５０７室

　　　　（〒112-8551　文京区春日1-13-27；東京メトロ丸の内線,

　　　　　南北線の「後楽園駅」または都営地下鉄大江戸線, 三田線の

　　　　「春日駅」から徒歩５分）

概　要：

In the first part of the talk I will explain our recent general results on the existence

of strong solutions of systems of particle systems.

Next, I will explain how these results are used to give a stochastic proof of

the Mayerhofer conjecture on the Wallach-Gindikin set $W$.

We exploit the fact that $(x_0,\beta) \in W$ if and only if $x_0$ is the starting point

and $2\beta$ is the drift of a Wishart process $X_t$ on the cone $\overline{Sym^+({\bf R},p)}$.

Our methods are based on the study of SDEs for the symmetric polynomials of $X_t$

and for the eigenvalues of $X_t$, i.e. the squared Bessel (BESQ) particle systems.

These results are based on the joint work with J. Malecki (Polytechnic Wroclaw).

問い合わせ先：中大・理工・物理　香取 眞理

　　　　　　　TEL: (03) 3817-1776

　　　　　　　E-mail: katori(at)phys.chuo-u.ac.jp

　　　　　　　居室　理工1号館5階 １５３８室