Painlev\'e kernels in Hermitian matrix models

Maurice Duits

Painlev\'e kernels in Hermitian matrix models

Mathematical Physics 2013-02-08 v1 Complex Variables math.MP

Authors: Maurice Duits

Abstract

After reviewing the Hermitian one matrix model, we will give a brief introduction to the Hermitian two matrix model and present a summary of some recent results on the asymptotic behavior of the two matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a $4\times 4$ Riemann-Hilbert problem related to Painlev\'e II equation. Also an open problem will be presented.

Cite

@article{arxiv.1302.1710,
  title  = {Painlev\'e kernels in Hermitian matrix models},
  author = {Maurice Duits},
  journal= {arXiv preprint arXiv:1302.1710},
  year   = {2013}
}

Comments

26 pages, 5 figures; This is a contribution to the Special Issue on Painlev\'e equations in the journal Constructive Approximation

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