Density of small singular values of the shifted real Ginibre ensemble

Autor:	Cipolloni, Giorgio, Erdős, László, Schröder, Dominik
Rok vydání:	2021
Předmět:	Mathematical Physics Mathematics - Probability 60B20 15B52 68W40
Druh dokumentu:	Working Paper
DOI:	10.1007/s00023-022-01188-8
Popis:	We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter $z$ as the dimension tends to infinity. For $z$ away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in [arXiv:1908.01653]. On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter $z$ becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula [arXiv:0707.2929] in a regime where the main contribution comes from a three dimensional saddle manifold. Comment: 15 pages, 4 figures. Updated references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.13720 Zobrazit plný text záznamu View this record from Arxiv