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2011 Explicit Expanders with Cutoff Phenomena
Eyal Lubetzky, Allan Sly
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Electron. J. Probab. 16: 419-435 (2011). DOI: 10.1214/EJP.v16-869

Abstract

The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph. The first example of a family of bounded-degree graphs where the random walk exhibits cutoff in total-variation was provided only very recently, when the authors showed this for a typical random regular graph. However, no example was known for an explicit (deterministic) family of expanders with this phenomenon. Here we construct a family of cubic expanders where the random walk from a worst case initial position exhibits total-variation cutoff. Variants of this construction give cubic expanders without cutoff, as well as cubic graphs with cutoff at any prescribed time-point.

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Eyal Lubetzky. Allan Sly. "Explicit Expanders with Cutoff Phenomena." Electron. J. Probab. 16 419 - 435, 2011. https://doi.org/10.1214/EJP.v16-869

Information

Accepted: 24 February 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60098
MathSciNet: MR2774096
Digital Object Identifier: 10.1214/EJP.v16-869

Subjects:
Primary: 60B10
Secondary: 05C81, 60G50, 60J10

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Vol.16 • 2011
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