Open Access
December 2014 Cores of Dirichlet forms related to random matrix theory
Hirofumi Osada, Hideki Tanemura
Proc. Japan Acad. Ser. A Math. Sci. 90(10): 145-150 (December 2014). DOI: 10.3792/pjaa.90.145


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.


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Hirofumi Osada. Hideki Tanemura. "Cores of Dirichlet forms related to random matrix theory." Proc. Japan Acad. Ser. A Math. Sci. 90 (10) 145 - 150, December 2014.


Published: December 2014
First available in Project Euclid: 4 December 2014

zbMATH: 1328.60181
MathSciNet: MR3290438
Digital Object Identifier: 10.3792/pjaa.90.145

Primary: 60B20 , 60J45 , 60J60

Keywords: Airy random point fields , Dirichlet forms , Dyson’s model , interacting Brownian motions in infinite-dimensions , logarithmic potentials , random matrices

Rights: Copyright © 2014 The Japan Academy

Vol.90 • No. 10 • December 2014
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