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Mathematical Physics
Title: Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel
(Submitted on 8 May 2022 (v1), last revised 27 Jul 2022 (this version, v2))
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 $1- \gamma$, $0 \leq \gamma <1$. 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.
Submission history
From: Dan Dai [view email][v1] Sun, 8 May 2022 15:27:34 GMT (1930kb,D)
[v2] Wed, 27 Jul 2022 02:47:55 GMT (1927kb,D)
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