Largest eigenvalue distribution in the double scaling limit of matrix models: A Coulomb fluid approach
High Energy Physics - Theory
2009-10-28 v1
Abstract
Using thermodynamic arguments we find that the probability that there are no eigenvalues in the interval (-s,\infty) in the double scaling limit of Hermitean matrix models is O(exp(-s^{2m+1})) as s\to+\infty.Here m=1,2,3.. determine the m^{th} multi-critical point of the level density:\sigma(x)\sim b[1-(x/b)^2]^{m-1/2} and b^2\sim N.Furthermore,the size of the transition zone where the eigenvalue density becomes vanishingly small at the tail of the spectrum is \sim N^{(m-3/2)/(2m+1)} in agreement with earlier work based on the string equation.
Cite
@article{arxiv.hep-th/9502123,
title = {Largest eigenvalue distribution in the double scaling limit of matrix models: A Coulomb fluid approach},
author = {Yang Chen and Kasper J. Eriksen and Craig A. Tracy},
journal= {arXiv preprint arXiv:hep-th/9502123},
year = {2009}
}
Comments
10 pages, no figures, to appear in J.Phys. A Lett. 1995