On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme

Abstract

AbstractWe consider random polynomial allocations of particles over N cells. Let τk, k ≥ 1, be the minimal number of trials when k particles hit the occupied cells. For the case N → ∞ the limit distribution of the random variable $\tau_k/\sqrt{N}$is found. An example of application of τk is given.