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 newconnected component of the eigenvalue density support appears away from other connectedcomponents. Unlike previously studied critical points, which correspond to rational singularitiesρ(x) ∼ xp/q classified by conformal minimal models and integrable hierarchies, this transition showslogarithmic and non-analytical behaviours. There is no critical exponent; instead, the power ofN changes in a sawtooth behaviour.