Moscow Mathematical Journal

Volume 23, Issue 4, October–December 2023 pp. 463–478.

Sub-Poissonian Estimates for Exponential Moments of Additive Functionals over Pairs of Particles with Respect to Determinantal and Symplectic Pfaffian Point Processes Governed by Entire Functions

Authors: A.I. Bufetov (1)
Author institution:Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia;
Department of Mathematics and Computer Sciences, St. Petersburg State University, St. Petersburg, Russia;
Institute of Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia;
Centre national de la recherche scientifique, France.

Summary:

The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles.

2020 Math. Subj. Class. Primary: 60G55; Secondary: 30D20.

Keywords: Determinantal processes, entire functions, occupation probabilities, distribution tails.

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