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Explicit Expanders with Cutoff Phenomena

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Explicit Expanders with Cutoff Phenomena
2.	Creator	Author's name, affiliation, country	Eyal Lubetzky; Microsoft Research; United States
2.	Creator	Author's name, affiliation, country	Allan Sly; Microsoft Research; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Cutoff phenomenon; Random walks; Expander graphs; Explicit constructions
3.	Subject	Subject classification	60B10, 60J10, 60G50, 05C81
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-02-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/869
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-869
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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