Proceedings of the Japan Academy, Series A, Mathematical Sciences

Cores of Dirichlet forms related to random matrix theory

Hirofumi Osada and Hideki Tanemura

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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

Permanent link to this document
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

Subjects
Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60J60: Diffusion processes [See also 58J65]

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

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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