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Glauber dynamics on nonamenable graphs: boundary conditions and mixing time

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Glauber dynamics on nonamenable graphs: boundary conditions and mixing time
2.	Creator	Author's name, affiliation, country	Alessandra Bianchi; Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Glauber dynamics; nonamenable graphs; spectral gap; mixing time
3.	Subject	Subject classification	82C20; 60K35; 82B20; 82C80
4.	Description	Abstract	We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n. This implies that the mixing time grows at most linearly in n. The class of graphs we consider includes hyperbolic graphs with sufficiently high degree, where the best upper bound on the mixing time of the free boundary dynamics is polynomial in n, with exponent growing with the inverse temperature. In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n. This provides a first example where the mixing time jumps from exponential to linear in n while passing from free to (+)-boundary condition. These results extend the analysis of Martinelli, Sinclair and Weitz to a wider class of nonamenable graphs.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2008-11-11
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/574
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-574
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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