Extrema of multinomial assignment process

TL;DR

This paper investigates the asymptotic behavior of the maximum and minimum values in a multinomial assignment process, providing results across various sparsity regimes to understand their expected extremes.

Contribution

It introduces new asymptotic analyses of the extrema in multinomial assignment processes under different sparsity conditions.

Findings

Derived asymptotic expectations for maxima and minima

Analyzed behavior across multiple sparsity regimes

Provided theoretical insights into large matrix assignment processes

Abstract

We study the asymptotic behavior of the expectation of the maxima and minima of random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes.