19 research outputs found
On bulk singularities in the random normal matrix model
We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to
study the distribution of eigenvalues close to a bulk singularity, i.e. a point
in the interior of the droplet where the density of the classical equilibrium
measure vanishes. We prove results to the effect that a certain "dominant part"
of the Taylor expansion determines the microscopic properties near a bulk
singularity. A description of the distribution is given in terms of a special
entire function, which depends on the nature of the singularity (a
Mittag-Leffler function in the case of a rotationally symmetric singularity).Comment: This version clarifies on the proof of Theorem
Rescaling Ward Identities in the Random Normal Matrix Model
We study spacing distribution for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward’s (or the “rescaled loop”) equation—an identity satisfied by all sequential limits of the rescaled one-point functions