Elliptic determinantal process of type A

• 成果类型: Article
• 署名作者: Katori, Makoto
• 署名单位: Chuo University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0581-9
• 发表日期: 2015
• 页码: 637-677
• 关键词: stochastic loewner evolution; brownian-motion; eigenvalues; IDENTITIES; paths; MODEL

摘要

We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of type , we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kernel is determined. By taking temporally homogeneous limits of the present elliptic determinantal process, trigonometric and hyperbolic versions of noncolliding diffusion processes are studied.