• Corpus ID: 238744212

Large gap asymptotics on annuli in the random normal matrix model

  title={Large gap asymptotics on annuli in the random normal matrix model},
  author={Christophe Charlier},
  • 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… 

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