On Asymptotic Expansion in the Random Allocation of Particles by Sets

TL;DR

This paper derives an Edgeworth type asymptotic expansion for the distribution of empty cells in a random particle allocation scheme, enhancing understanding of the local central limit theorem in this context.

Contribution

It introduces a new asymptotic expansion for the distribution of empty cells in a set-based particle allocation scheme, extending classical limit theorems.

Findings

Derived an Edgeworth expansion for empty cell distribution

Enhanced local CLT understanding in particle allocation models

Provided asymptotic formulas for large particle sets

Abstract

We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is derived.