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2012 Convergence of mixing times for sequences of random walks on finite graphs
David Croydon, Ben Hambly, Takashi Kumagai
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Electron. J. Probab. 17: 1-32 (2012). DOI: 10.1214/EJP.v17-1705


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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David Croydon. Ben Hambly. Takashi Kumagai. "Convergence of mixing times for sequences of random walks on finite graphs." Electron. J. Probab. 17 1 - 32, 2012.


Accepted: 5 January 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.05207
MathSciNet: MR2869250
Digital Object Identifier: 10.1214/EJP.v17-1705

Primary: 60J10
Secondary: 05C80

Keywords: fractal graph , Galton-Watson tree , Gromov-Hausdorff convergence , Mixing , random graph , Random walk


Vol.17 • 2012
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