TY - JOUR
T1 - Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel
AU - Dai, Dan
AU - Zhai, Yu
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
KW - confluent hypergeometric kernel
KW - Fredholm determinant
KW - gap probability
KW - PAINLEVE-II
KW - UNIVERSALITY
KW - TOEPLITZ
KW - AIRY
KW - DISTRIBUTIONS
KW - SOLVABILITY
KW - POLYNOMIALS
KW - ENSEMBLES
KW - HANKEL
KW - BESSEL
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U2 - 10.1111/sapm.12528
DO - 10.1111/sapm.12528
M3 - 21_Publication in refereed journal
VL - 149
SP - 1032
EP - 1085
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
SN - 0022-2526
IS - 4
ER -