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arXiv · 2205.00721

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

Christophe Charlier·Jonatan Lenells
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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 $n^{-\smash{\frac{1}{2}}}$, 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.

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Christophe Charlier, Jonatan Lenells. 2022-05-02. Exponential moments for disk counting statistics of random normal matrices in the critical regime. https://doi.org/10.1088/1361-6544%2Facb47c

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