Maximal probabilities of convolution powers of discrete uniform distributions

TL;DR

This paper establishes optimal bounds on the maximum probabilities of convolution powers of discrete uniform distributions, showing how these probabilities scale with the number of convolutions.

Contribution

It provides the first sharp constant bounds for the maximal probabilities of convolution powers of discrete uniform distributions.

Findings

Proved optimal constant bounds over root n for maximal probabilities.

Established the asymptotic behavior of convolution powers.

Enhanced understanding of discrete uniform distribution convolutions.

Abstract

We prove optimal constant over root $n$ upper bounds for the maximal probabilities of $n$th convolution powers of discrete uniform distributions.