Cores of Dirichlet forms related to random matrix theory

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Hirofumi Osada¹  Hideki Tanemura² 

[1] Faculty of Mathematics, Kyushu University;Department of Mathematics and Informatics, Faculty of Science, Chiba University

关键词: Random matrices;    Dyson’s model;    interacting Brownian motions in infinitedimensions;    Airy random point fields;    logarithmic potentials;    Dirichlet forms.;   

DOI  :  10.3792/pjaa.90.145

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms describing interacting Brownian motion in infinite dimensions. Typical examples of these stochastic dynamics are Dyson’s Brownian motion and Airy interacting Brownian motion. Both particle systems have logarithmic interaction potentials, and naturally arise from random matrix theory. The results of the present paper will be used in a forth coming paper to prove the identity of the infinite-dimensional stochastic dynamics related to the random matrix theories constructed by apparently different methods: the method of space-time correlation functions and that of stochastic analysis.

【 授权许可】

Unknown