# Large gap asymptotics on annuli in the random normal matrix model

@inproceedings{Charlier2021LargeGA, title={Large gap asymptotics on annuli in the random normal matrix model}, author={Christophe Charlier}, year={2021} }

We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process. In this paper, we prove that the probability that no points lie on any number of annuli centered at $0$ satisfies large $n$ asymptotics of the form \begin{align*} \exp \bigg( C_{1} n^{2} + C_{2} n \log n + C_{3} n + C_{4} \sqrt{n} + C_{5}\log n + C_{6} + \mathcal{F}_{n} + \mathcal{O}\big( n^{-\frac{1}{12}}\big)\bigg…

## 4 Citations

### On the almost‐circular symplectic induced Ginibre ensemble

- MathematicsStudies in Applied Mathematics
- 2022

We consider the symplectic‐induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost‐circular regime where most of the points lie…

### Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases

- Materials ScienceJournal of Statistical Physics
- 2022

An exact map was established by Lacroix-A-Chez-Toine et al. in (Phys Rev A 99(2):021602, 2019) between the N complex eigenvalues of complex non-Hermitian random matrices from the Ginibre ensemble,…

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

- MathematicsNonlinearity
- 2023

We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag–Leffler ensemble, where n is the number of points of the process and m is…

### Random normal matrices in the almost-circular regime

- MathematicsBernoulli
- 2023

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow"band"around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For…

### Partition Functions of Determinantal and Pfaffian Coulomb Gases with Radially Symmetric Potentials

- Computer ScienceCommunications in Mathematical Physics
- 2023

This work considers random normal matrix and planar symplectic ensembles, which can be interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian structures, respectively, and derives the asymptotic expansions of the log-partition functions up to and including the O(1)-terms as the number of particles increases.

### The elliptic Ginibre ensemble: A unifying approach to local and global statistics for higher dimensions

- MathematicsJournal of Mathematical Physics
- 2023

The elliptic Ginibre ensemble of complex non-Hermitian random matrices allows us to interpolate between the rotationally invariant Ginibre ensemble and the Gaussian unitary ensemble of Hermitian…

### Planar equilibrium measure problem in the quadratic fields with a point charge

- Mathematics
- 2023

. We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit shape of the associated droplets. This particularly…

### Determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials

- Mathematics
- 2022

. We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point…

### Spherical induced ensembles with symplectic symmetry

- Mathematics
- 2022

. We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive…

### Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials

- ArtCommunications in Mathematical Physics
- 2022

Consider the subspace Wn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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