ON THE GENERATING FUNCTION OF THE PEARCEY PROCESS

• 成果类型: Article
• 署名作者: Charlier, Christophe; Moreillon, Philippe
• 署名单位: Royal Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1890
• 发表日期: 2023
• 页码: 3240-3277
• 关键词: level-spacing distributions; RANDOM MATRICES; external source; UNIVERSALITY; eigenvalues; bessel; airy

摘要

The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number m of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of 6m + 2 coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some results of Dai, Xu, and Zhang, which correspond to m = 1.