Edge Universality for Nonintersecting Brownian Bridges

2020/11/03 by Jiaoyang Huang, Huang, Jiaoyang
Mathematics · #60B20 #60K35 #70S05 #Advanced Combinatorial Mathematics #Brownian motion #Condensed matter physics #FOS: Mathematics #Mathematics #Physics #Probability (math.PR) #Random Matrices and Applications #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Universality (dynamical systems) #math.PR #msc:60B20 #msc:60K35 #msc:70S05

paper · pdf · doi:10.48550/arxiv.2011.01752

56 pages, 4 figures. Draft version, comments are welcome

arxiv created 2020/11/03 · openalex publication_date 2020/11/03 · arxiv updated 2020/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from a₁≤ a₂≤ ⋯ ≤ a_n at time t=0 and ending at b₁≤ b₂≤ ⋯≤ b_n at time t=1, where μ_An=(1/n)∑_iδ_ai, μ_Bn=(1/n)∑_i δ_bi are discretization of probability measures μ_A, μ_B. Under regularity assumptions of μ_A, μ_B, we show as the number of particles n goes to infinity, fluctuations of extreme particles at any time 0<t<1, after proper rescaling, are asymptotically universal, converging to the Airy point process.

Citations

• Random matrices and determinantal processes
• Asymptotic analysis of the two matrix model with a quartic potential
• Universal singularity at the closure of a gap in a random matrix theory
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• From interacting particle systems to random matrices
• Edge statistics of Dyson Brownian motion
• Lectures notes on compact Riemann surfaces
• The directed landscape

Related

• Brownian bridge limit of path measures in the upper tail of KPZ models
• Dynamics at the edge for independent diffusing particles
• Universal edge fluctuations of discrete interlaced particle systems
• Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III
• Brownian Gibbs property for Airy line ensembles