Universality of the Stochastic Bessel Operator

• 成果类型: Article
• 署名作者: Rider, Brian; Waters, Patrick
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0888-z
• 发表日期: 2019
• 页码: 97-140
• 关键词: random matrices; ensembles; spectrum; models; edge

摘要

We establish universality at the hard edge for general beta ensembles assuming that: the background potential V is a polynomial such that x -> V(x(2)) is strongly convex, beta >= 1, and the dimension-difference parameter a >= 0. The method rests on the corresponding tridiagonal matrix models, showing that their appropriate continuum scaling limit is given by the Stochastic Bessel Operator. As conjectured in Edelman and Sutton (J Stat Phys 127:1121-1165, 2007) and rigorously established in Ramirez and Rider (Commun Math Phys 288:887-906, 2009), the latter characterizes the hard edge in the case of linear potential and all beta (the classical beta-Laguerre ensembles).