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Convergence of mixing times for sequences of random walks on finite graphs


 
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1. Title Title of document Convergence of mixing times for sequences of random walks on finite graphs
 
2. Creator Author's name, affiliation, country David A Croydon; University of Warwick; United Kingdom
 
2. Creator Author's name, affiliation, country Ben M Hambly; University of Oxford; United Kingdom
 
2. Creator Author's name, affiliation, country Takashi Kumagai; Kyoto University; Japan
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walk; mixing; Gromov-Hausdorff convergence; random graph; Galton-Watson tree; fractal graph
 
3. Subject Subject classification 60J10; 05C80
 
4. Description Abstract

We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a suitable Gromov-Hausdorff sense. With this result we are able to establish the convergence of the mixing times on the largest component of the Erdős-Rényi random graph in the critical window, sharpening previous results for this random graph model. Our results also enable us to establish convergence in a number of other examples, such as finitely ramified fractal graphs, Galton-Watson trees and the range of a high-dimensional random walk.
 
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7. Date (YYYY-MM-DD) 2012-01-05
 
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/1705
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1705
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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