Universal distribution of random matrix eigenvalues near the "birth of a cut" transition

Abstract

We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which correspond to rational singularities \rho(x)\sim x^{p/q} classified by conformal minimal models and integrable hierarchies, this transition shows logarithmic and non-analytical behaviours. There is no critical exponent, instead, the power of N changes in a saw teeth behaviour.