Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

On sensitivity of uniform mixing times

Jonathan Hermon

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We show that the order of the $L_{\infty}$-mixing time of simple random walks on a sequence of uniformly bounded degree graphs of size $n$ may increase by an optimal factor of $\Theta(\log\log n)$ as a result of a bounded perturbation of the edge weights. This answers a question and a conjecture of Kozma.


Nous montrons que le temps de mélange pour la distance $L_{\infty}$ d’une marche aléatoire sur une suite de graphe de taille $n$ et de degré uniformément borné peut être multiplié par un facteur d’ordre $\log\log n$ (optimal) en perturbant le poids des arrêtes du graphe de manière uniformément bornée. Ceci résout une question et une conjecture de Kozma.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 1 (2018), 234-248.

Received: 6 July 2016
Revised: 26 September 2016
Accepted: 17 October 2016
First available in Project Euclid: 19 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Sensitivity Mxing-time Sensitivity of mixing times Hitting times


Hermon, Jonathan. On sensitivity of uniform mixing times. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 1, 234--248. doi:10.1214/16-AIHP802.

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