Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel

2022/05/08 by Dan Dai, Dai, Dan, Yu Zhai +1 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2205.03897

openalex publication_date 2022/05/08 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed independently with probability 1- γ, 0 ≤ γ<1. We derive asymptotics of the deformed Fredholm determinant when the gap interval tends to infinity, up to and including the constant term. As an application of our results, we establish a central limit theorem for the eigenvalue counting function and a global rigidity upper bound for its maximum deviation.

Cited by

• Asymptotics of Fredholm determinant solutions of the noncommutative Painlevé II equation

Related

• On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities
• Confluent hypergeometric kernel determinant on multiple large intervals
• Central limit theorem for the determinantal point process with the confluent hypergeometric kernel
• Asymptotics of the confluent hypergeometric process with a varying external potential in the super-exponential region
• The asymptotics a Bessel-kernel determinant which arises in Random Matrix Theory