Asymptotic Properties of Random Contingency Tables with Uniform Margin

TL;DR

This paper investigates the asymptotic behavior of large random contingency tables with fixed uniform margins, providing insights into their probabilistic structure as the table size grows.

Contribution

It offers new theoretical results on the asymptotic properties of random contingency tables with uniform margins as the dimension increases.

Findings

Asymptotic distribution characterized for large tables

Limit theorems established for row and column sums

Insights into the probabilistic structure of contingency tables

Abstract

Let $C\geq 2$ be a positive integer. Consider the set of $n\times n$ non-negative integer matrices whose row sums and column sums are all equal to $Cn$ and let $X=(X_{ij})_{1\leq i,j\leq n}$ be uniformly distributed on this set. This $X$ is called the random contingency table with uniform margin. In this paper, we study various asymptotic properties of $X=(X_{ij})_{1\leq i,j\leq n}$ as $n\to\infty$.