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 $\log q=o\left (\frac{ \sqrt{ \log n}}{ \log \log n}\right )$.
Categories: math.PR math.CO