The hard-to-soft edge transition: exponential moments, central limit theorems and rigidity

2021/04/23 by Christophe Charlier, Jonatan Lenells, Charlier, Christophe +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2104.11494

openalex publication_date 2021/04/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter α. For this point process, we obtain 1) exponential moment asymptotics, up to and including the constant term, 2) asymptotics for the expectation and variance of the counting function, 3) several central limit theorems and 4) a global rigidity upper bound.

Related

• The random matrix hard edge: rare events and a transition
• Asymptotic expansion of the hard-to-soft edge transition
• The asymptotics a Bessel-kernel determinant which arises in Random Matrix Theory
• Exponential moments and piecewise thinning for the Bessel point process
• Large gap asymptotics at the hard edge for product random matrices and\n Muttalib-Borodin ensembles