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arXiv · 1808.06157

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

Evita Nestoridi·Oanh Nguyen
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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 $\log q=o\left (\frac{\sqrt{\log n}}{\log \log n}\right )$.

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Evita Nestoridi, Oanh Nguyen. 2018-08-19. On the mixing time of the Diaconis--Gangolli random walk on contingency tables over $\mathbb{Z}/ q \mathbb{Z}$. https://arxiv.org/abs/1808.06157

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