## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Cores of Dirichlet forms related to random matrix theory

#### Abstract

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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 10 (2014), 145-150.

Dates
First available in Project Euclid: 4 December 2014

https://projecteuclid.org/euclid.pja/1417707835

Digital Object Identifier
doi:10.3792/pjaa.90.145

Mathematical Reviews number (MathSciNet)
MR3290438

Zentralblatt MATH identifier
1328.60181

#### Citation

Osada, Hirofumi; Tanemura, Hideki. Cores of Dirichlet forms related to random matrix theory. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 10, 145--150. doi:10.3792/pjaa.90.145. https://projecteuclid.org/euclid.pja/1417707835

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