Gaussian complex zeroes are not always normal: limit theorems on the disc

Autor:	Buckley, Jeremiah, Nishry, Alon
Rok vydání:	2021
Předmět:	Mathematics - Probability Mathematical Physics Mathematics - Complex Variables Primary: 30B20 60F05 60G15. Secondary: 60G55
Zdroj:	Prob. Math. Phys. 3 (2022) 675-706
Druh dokumentu:	Working Paper
DOI:	10.2140/pmp.2022.3.675
Popis:	We study the zeroes of a family of random holomorphic functions on the unit disc, distinguished by their invariance with respect to the hyperbolic geometry. Our main finding is a transition in the limiting behaviour of the number of zeroes in a large hyperbolic disc. We find a normal distribution if the covariance decays faster than a certain critical value. In contrast, in the regime of 'long-range dependence' when the covariance decays slowly, the limiting distribution is skewed. For a closely related model we emphasise a link with Gaussian multiplicative chaos. Comment: 27 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.12598 Zobrazit plný text záznamu View this record from Arxiv