Strong characterization for the Airy line ensemble

• 成果类型: Article; Early Access
• 署名作者: Aggarwal, Amol; Huang, Jiaoyang
• 署名单位: Columbia University; University of Pennsylvania
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01381-6
• 发表日期: 2025
• 关键词: brownian-motion; semicircle law; fluctuations; UNIVERSALITY; spectrum; polymer; tilings; limit; delocalization; asymptotics

摘要

In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove that if l = (L-1, L-2, ...) is a line ensemble satisfying the Brownian Gibbs property, such that for any epsilon > 0 there exists a constant R (epsilon) > 0 with P[|L-1(t) + 2(-1/2)t(2)|<= epsilon t(2) + R(epsilon)] >= 1-epsilon, for all t is an element of R, then L is the parabolic Airy line ensemble, up to an independent affine shift. Specializing this result to the case when L(t) + 2-(1/2)t(2) is translation-invariant confirms a prediction of Okounkov and Sheffield from 2006 and Corwin-Hammond from 2014.