On Airy solutions of P$_\mathrm{II}$ and the complex cubic ensemble of random matrices, II
Mathematical Physics
2024-03-08 v2 Classical Analysis and ODEs
math.MP
Abstract
We describe the pole-free regions of the one-parameter family of special solutions of P, the second Painlev\'e 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.
Keywords
Cite
@article{arxiv.2403.03023,
title = {On Airy solutions of P$_\mathrm{II}$ and the complex cubic ensemble of random matrices, II},
author = {Ahmad Barhoumi and Pavel Bleher and Alfredo Deaño and Maxim L. Yattselev},
journal= {arXiv preprint arXiv:2403.03023},
year = {2024}
}