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May 2020 On the mixing time of the Diaconis–Gangolli random walk on contingency tables over $\mathbb{Z}/q\mathbb{Z}$
Evita Nestoridi, Oanh Nguyen
Ann. Inst. H. Poincaré Probab. Statist. 56(2): 983-1001 (May 2020). DOI: 10.1214/19-AIHP991

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 $\log q=o(\frac{\sqrt{\log n}}{ \log\log n})$.

La marche aléatoire de Diaconis–Gangolli est un algorithme qui génère un graphe aléatoire à degrés prescrits, de loi presque uniforme. Dans cet article, nous étudions le temps de mélange de cette marche aléatoire restreinte aux tableaux de contingence de taille $n\times n$ sur $\mathbb{Z}/q\mathbb{Z}$. Nous montrons que la marche aléatoire présente une transition abrupte (cutoff) à $\frac{n^{2}}{4(1-\cos(\frac{2\pi}{q}))}\log n$, où $\log q=o(\frac{\sqrt{\log n}}{\log\log n})$.

Citation

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Evita Nestoridi. Oanh Nguyen. "On the mixing time of the Diaconis–Gangolli random walk on contingency tables over $\mathbb{Z}/q\mathbb{Z}$." Ann. Inst. H. Poincaré Probab. Statist. 56 (2) 983 - 1001, May 2020. https://doi.org/10.1214/19-AIHP991

Information

Received: 15 October 2018; Revised: 12 February 2019; Accepted: 2 April 2019; Published: May 2020
First available in Project Euclid: 16 March 2020

zbMATH: 07199887
MathSciNet: MR4076773
Digital Object Identifier: 10.1214/19-AIHP991

Subjects:
Primary: 60J10
Secondary: 60C05, 60G42

Rights: Copyright © 2020 Institut Henri Poincaré

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Vol.56 • No. 2 • May 2020
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