Poisson Limit Theorems in an Allocation Scheme with an Even Number of Particles in Each Cell

Abstract

© 2020, Pleiades Publishing, Ltd. Abstract: We consider an allocation scheme of 2n distinguishable particles by $$N$$ different cells under the condition than each cell contains an even number of particles. We show that this scheme is a general allocation scheme defined by the random variable ξi with the distribution (Formula Presented.). Let μ2r(N,K,n) be a number of cells from the first K cells that contain 2r particles. We prove that under some types of convergence of n,K,N to infinity μ2r(N,K,n) converges in distribution to the Poisson random variable. The limit Poisson random variable is described.