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

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