Large gap asymptotics on annuli in the random normal matrix model
نویسندگان
چکیده
Abstract We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is two-parameter generalization of complex Ginibre process. In this paper, we prove that probability no points lie on any number annuli centered at 0 satisfies large n asymptotics form $$\begin{aligned} \exp \Bigg ( C_{1} n^{2} + C_{2} \log C_{3} C_{4} \sqrt{n} C_{5}\log C_{6} {\mathcal {F}}_{n} \mathcal {O}\Big n^{-\frac{1}{12}}\Big )\Bigg ), \end{aligned}$$ exp ( C 1 n 2 + log 3 4 5 6 F O - 12 ) , where determine constants $$C_{1},\ldots ,C_{6}$$ … explicitly, as well oscillatory term $${\mathcal {F}}_{n}$$ order 1. also allow one annulus to be disk, unbounded. For process, improve best known results: (i) when hole region only ,C_{4}$$ were previously known, (ii) an unbounded annulus, $$C_{1},C_{2},C_{3}$$ (iii) regular bulk, $$C_{1}$$ was known. general values our parameters, even new. A main discovery work given terms Jacobi theta function. As far know first time function appears gap problem
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2023
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-023-02603-z