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Convergence of mixing times for sequences of random walks on finite graphs
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Croydon, David A., Hambly, Ben M. and Kumagai, Takashi (2012) Convergence of mixing times for sequences of random walks on finite graphs. Electronic Journal of Probability, Vol.17 . article no.3. doi:10.1214/EJP.v17-1705 ISSN 1083-6489.
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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 Erdos-Renyi 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Graph theory | ||||
Journal or Publication Title: | Electronic Journal of Probability | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 1083-6489 | ||||
Official Date: | 5 January 2012 | ||||
Dates: |
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Volume: | Vol.17 | ||||
Page Range: | article no.3 | ||||
DOI: | 10.1214/EJP.v17-1705 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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