Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications

TL;DR

This paper establishes large and moderate deviation principles for the distribution of empirical means of discrete i.i.d. variables conditioned on their sum, with applications to combinatoric problems.

Contribution

It introduces deviation principles for conditioned sums of discrete variables, extending probabilistic tools to combinatoric contexts.

Findings

Large deviation principles proved for conditioned sums

Moderate deviation principles established

Applications demonstrated in combinatoric problems

Abstract

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.