Journal
ACTA MATHEMATICA SINICA-ENGLISH SERIES
Volume 39, Issue 8, Pages 1580-1596Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10114-023-1570-7
Keywords
Discrete ensemble; precise deviation; random growth model; Riemann-Hilbert problem
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We study precise deviations for discrete ensembles. For the case of beta=2, we establish an asymptotic formula for the Christoffel-Darboux kernel of the discrete orthogonal polynomials on an infinite regular lattice with weight e(-NV(x)). Using this asymptotic formula, we obtain the precise deviations of the extreme value for the corresponding ensemble.
We consider precise deviations for discrete ensembles. For beta = 2 case, we first establish an asymptotic formula of the Christoffel-Darboux kernel of the discrete orthogonal polynomials on an infinite regular lattice with weight e(-NV(x)). Then we use the asymptotic formula to get the precise deviations of the extreme value for corresponding ensemble.
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