BULK PROPERTIES OF THE AIRY LINE ENSEMBLE

• 成果类型: Article
• 署名作者: Dauvergne, Duncan; Virag, Balint
• 署名单位: Princeton University; University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1492
• 发表日期: 2021
• 页码: 1738-1777
• 关键词: brownian-motion; eigenvalues; particles; sine

摘要

The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools, which allow for precise probabilistic analysis of the Airy line ensemble. The two main theorems are a representation in terms of independent Brownian bridges connecting a fine grid of points, and a modulus of continuity result for all lines. Along the way, we give tail bounds and moduli of continuity for nonintersecting Brownian ensembles, and a quick proof of tightness for Dyson's Brownian motion converging to the Airy line ensemble.