Exponential moments for disk counting statistics of random normal matrices in the critical regime

Abstract

We obtain large $n$ asymptotics for the $m$-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the critical regime where all disk boundaries are merging at speed $n^{-\frac{1}{2}}$, either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large $n$ asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large $n$ asymptotics for $n\times n$ determinants with merging planar discontinuities.

23 pages, 1 figure

References in corpus (3)

• Counting statistics for non-interacting fermions in a rotating trap
• Universality of the number variance in rotational invariant two-dimensional Coulomb gases
• Laguerre Unitary Ensembles with Jump Discontinuities, PDEs and the Coupled Painlevé V System

Cited by in corpus (5)

• Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials
• Universality of the number variance in rotational invariant two-dimensional Coulomb gases
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling
• Universality for fluctuations of counting statistics of random normal matrices