Cores of dirichlet forms related to random matrix theory

Hirofumi Osada, Hideki Tanemura

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)145-150
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume90
Issue number10
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes

Fingerprint

Dirichlet Form
Random Matrix Theory
Brownian motion
Stochastic Dynamics
Infinite Dimensions
Stochastic Analysis
Particle System
Configuration Space
Correlation Function
Logarithmic
Space-time
Polynomial
Interaction

Keywords

  • Airy random point fields
  • Dirichlet forms
  • Dyson's model
  • Interacting brownian motions in infinitedimensions
  • Logarithmic potentials
  • Random matrices

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cores of dirichlet forms related to random matrix theory. / Osada, Hirofumi; Tanemura, Hideki.

In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 90, No. 10, 01.01.2014, p. 145-150.

Research output: Contribution to journalArticle

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