### 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 language | English |
---|---|

Pages (from-to) | 145-150 |

Number of pages | 6 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 90 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 90, no. 10, pp. 145-150. https://doi.org/10.3792/pjaa.90.145

}

TY - JOUR

T1 - Cores of dirichlet forms related to random matrix theory

AU - Osada, Hirofumi

AU - Tanemura, Hideki

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Airy random point fields

KW - Dirichlet forms

KW - Dyson's model

KW - Interacting brownian motions in infinitedimensions

KW - Logarithmic potentials

KW - Random matrices

UR - http://www.scopus.com/inward/record.url?scp=84919350953&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919350953&partnerID=8YFLogxK

U2 - 10.3792/pjaa.90.145

DO - 10.3792/pjaa.90.145

M3 - Article

AN - SCOPUS:84919350953

VL - 90

SP - 145

EP - 150

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 10

ER -