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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112595We 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 ρ(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.Latex, 34 pages, 5 figuresMathematical PhysicsStatistical MechanicsExactly Solvable and Integrable SystemsUniversal distribution of random matrix eigenvalues near the "birth of a cut" transitiontext