2023/12/31 by Alexander I. Bufetov, Bufetov, Alexander I.
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2401.00527
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.