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February 2018 On sensitivity of uniform mixing times
Jonathan Hermon
Ann. Inst. H. Poincaré Probab. Statist. 54(1): 234-248 (February 2018). DOI: 10.1214/16-AIHP802


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.


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Jonathan Hermon. "On sensitivity of uniform mixing times." Ann. Inst. H. Poincaré Probab. Statist. 54 (1) 234 - 248, February 2018.


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

zbMATH: 06868370
MathSciNet: MR3765888
Digital Object Identifier: 10.1214/16-AIHP802

Primary: 60J10

Keywords: hitting times , Mxing-time , Sensitivity , Sensitivity of mixing times

Rights: Copyright © 2018 Institut Henri Poincaré


Vol.54 • No. 1 • February 2018
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