• Corpus ID: 238744212

# 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}
}
• C. Charlier
• Published 13 October 2021
• Mathematics, Computer Science
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

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## References

SHOWING 1-10 OF 76 REFERENCES

• Mathematics
• 2014
AbstractWe obtain large N asymptotics for the random matrix partition function $$Z_N(V)=\int_{\mathbb{R}^N} \prod_{i < • Mathematics Acta Mathematica • 2021 We prove that the planar normalized orthogonal polynomials P_{n,m}(z) of degree n with respect to an exponentially varying planar measure e^{-2mQ(z)}\mathrm{dA}(z) enjoy an asymptotic expansion • Mathematics • 2016 We study the hole probabilities of the infinite Ginibre ensemble {\mathcal X}_{\infty}, a determinantal point process on the complex plane with the kernel \mathbb K(z,w)= \frac{1}{\pi}e^{z\bar • Mathematics Potential Analysis • 2021 In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the • Mathematics • 2016 AbstractWe consider the orthogonal polynomials,$${\{P_n(z)\}_{n=0,1,\ldots}}$${Pn(z)}n=0,1,…, with respect to the measure$$|z-a|^{2c} e^{-N|z|^2}dA(z)$$|z-a|2ce-N|z|2dA(z)supported over the whole • Mathematics • 2012 We consider eigenvalues of a product of n non-Hermitian, independent random matrices. Each matrix in this product is of size N×N with independent standard complex Gaussian variables. The eigenvalues • Materials Science Communications in Mathematical Physics • 2021 The limiting process that arises at the hard edge of Muttalib–Borodin ensembles is considered and the constants c and C can be expressed in terms of Barnes’ G-function. • Mathematics Communications in Mathematical Physics • 2021 The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a • Mathematics Physical review. E • 2019 The Ginibre ensemble of N×N complex random matrices is studied and the intermediate deviation function that describes these intermediate fluctuations can be computed explicitly and it is demonstrated that it is universal, i.e., it holds for a large class of complexrandom matrices. • Mathematics • 2003 AbstractThe ‘hoe probability’ that a random entire function$$\psi (z) = \sum\limits_{k = 0}^\infty {\zeta _k \frac{{z^k }}{{\sqrt {k!} }}} , where ζ0, ζ1, ... are Gaussian i.i.d. random