On Airy solutions of P_II and the complex cubic ensemble of random matrices, II

2024/03/05 by Ahmad Barhoumi, Barhoumi, Ahmad, Pavel Bleher +5
Engineering · Mathematics · #15B52 #33C10 #33C47 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #advanced mathematical theories #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2403.03023

openalex publication_date 2024/03/05 · openalex created_date 2024/03/07 · openalex updated_date 2026/08/01

Abstract

We describe the pole-free regions of the one-parameter family of special solutions of P_II, the second Painlevé equation, constructed from the Airy functions. This is achieved by exploiting the connection between these solutions and the recurrence coefficients of orthogonal polynomials that appear in the analysis of the ensemble of random matrices corresponding to the cubic potential.

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