On the mixing time of the Diaconis--Gangolli random walk on contingency tables over $\mathbb{Z}/q\mathbb{Z}$

Abstract

The Diaconis--Gangolli random walk is an algorithm that generates an almost uniform random graph with prescribed degrees. In this paper, we study the mixing time of the Diaconis--Gangolli random walk restricted on $n\times n$ contingency tables over $\mathbb{Z}/q\mathbb{Z}$. We prove that the random walk exhibits cutoff at $\frac{n^2}{4(1-\cos \frac{2\pi }{q})}\log n,$ when $\log q=o\left(\frac{\sqrt{\log n}}{\log \log n}\right)$.