Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: Airy random point field

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Osada, Hirofumi

关键词: Interacting Brownian particles;    Random matrices;    Coulomb potentials;    Infinitely many particle systems;    Diffusions;    Airy random point field;    Quasi-Gibbs property;   

DOI  :  10.1016/j.spa.2012.11.002

来源: Elsevier

【 摘 要 】

We give a new sufficient condition of the quasi-Gibbs property. This result is a refinement of one given in a previous paper (Osada (in press) [18]), and will be used in a forthcoming paper to prove the quasi-Gibbs property of Airy random point fields (RPFs) and other RPFs appearing under soft-edge scaling. The quasi-Gibbs property of RPFs is one of the key ingredients to solve the associated infinite-dimensional stochastic differential equation (ISDE). Because of the divergence of the free potentials and the interactions of the finite particle approximation under soft-edge scaling, the result of the previous paper excludes the Airy RPFs, although Airy RPFs are the most significant RPFs appearing in random matrix theory. We will use the result of the present paper to solve the ISDE for which the unlabeled equilibrium state is the Airy(beta) RPF with beta = 1, 2, 4. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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