Gap probability for products of random matrices in the critical regime

被引:1
作者
Berezin, Sergey [1 ,2 ]
Strahov, Eugene [1 ]
机构
[1] Hebrew Univ Jerusalem, Dept Math, IL-91904 Jerusalem, Israel
[2] VA Steklov Math Inst RAS, 27 Fontanka, St Petersburg 191023, Russia
关键词
Products of random matrices; Gap probabilities; Riemann-Hilbert problems; Determinantal point processes; Singular value statistics; LEVEL-SPACING DISTRIBUTIONS; TAU-FUNCTION THEORY; FREDHOLM DETERMINANTS; PAINLEVE EQUATIONS; SINGULAR-VALUES; HARD EDGE; ASYMPTOTICS; UNIVERSALITY;
D O I
10.1016/j.jat.2021.105687
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The singular values of a product of M independent Ginibre matrices of size N x N form a determinantal point process. Near the soft edge, as both M and N go to infinity in such a way that M/N -> alpha, alpha > 0, a scaling limit emerges. We consider a gap probability for the corresponding limiting determinantal process, namely, the probability that there are no particles in the interval (a, +infinity). We derive a Tracy-Widom-like formula in terms of the unique solution of a certain matrix Riemann- Hilbert problem of size 2 x 2. The right-tail asymptotics for this solution is obtained by the Deift-Zhou non-linear steepest descent analysis. (c) 2021 Elsevier Inc. All rights reserved.
引用
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页数:29
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