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

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) similar to 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 sawtooth behaviour.