The bead process for beta ensembles
成果类型：
Article
署名作者：
Najnudel, Joseph; Virag, Balint
署名单位：
University of Bristol; University of Toronto
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-021-01034-8
发表日期：
2021
页码：
589-647
关键词：
摘要：
The bead process introduced by Boutillier is a countable interlacing of the Sine(2) point processes. We construct the bead process for general Sine(beta) processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite beta corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virag in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).