Point processes, hole events, and large deviations: random complex zeros and Coulomb gases

Autor:	Ghosh, Subhro, Nishry, Alon
Rok vydání:	2018
Předmět:	Mathematics - Probability Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables
Druh dokumentu:	Working Paper
Popis:	We consider particle systems (also known as point processes) on the line and in the plane, and are particularly interested in "hole" events, when there are no particles in a large disk (or some other domain). We survey the extensive work on hole probabilities and the related large deviation principles (LDP), which has been undertaken mostly in the last two decades. We mainly focus on the recent applications of LDP-inspired techniques to the study of hole probabilities, and the determination of the most likely configurations of particles that have large holes. As an application of this approach, we illustrate how one can confirm some of the predictions of Jancovici, Lebowitz, and Manificat for large fluctuation in the number of points for the (two-dimensional) $\beta$-Ginibre ensembles. We also discuss some possible directions for future investigations. Comment: To appear in Constructive Approximation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.03268 Zobrazit plný text záznamu View this record from Arxiv