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Mixing and relaxation time for random walk on wreath product graphs

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Mixing and relaxation time for random walk on wreath product graphs
2.	Creator	Author's name, affiliation, country	Júlia Komjáthy; Budapest University of Technology and Economics; Hungary
2.	Creator	Author's name, affiliation, country	Yuval Peres; Microsoft Research; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random Walk, Wreath Product Graphs, Mixing Time, Relaxation Time
3.	Subject	Subject classification	60J10, 60D05, 37A25
4.	Description	Abstract	Suppose that G and H are finite, connected graphs, G regular, X is a lazy random walk on G and Z is a reversible ergodic Markov chain on H. The generalized lamplighter chain X* associated with X and Z is the random walk on the wreath product H\wr G, the graph whose vertices consist of pairs (f,x) where f=(f_v)_{v\in V(G)} is a labeling of the vertices of G by elements of H and x is a vertex in G. In each step, X* moves from a configuration (f,x) by updating x to y using the transition rule of X and then independently updating both f_x and f_y according to the transition probabilities on H; f_z for z different of x,y remains unchanged. We estimate the mixing time of X* in terms of the parameters of H and G. Further, we show that the relaxation time of X* is the same order as the maximal expected hitting time of G plus |G| times the relaxation time of the chain on H.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-07-30
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/2321
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2321
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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