Mixed and Isoperimetric Estimates on the Log-Sobolev Constants of Graphs and Markov Chains

Two types of lower bounds are obtained on the log-Sobolev constants of graphs and Markov chains. The first is a mixture of spectral gap and logarithmic isoperimetric constant, the second involves the Gaussian isoperimetric constant. The sharpness of both types of bounds is tested on some examples. Product generalizations of some of these results are also briefly given.

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Received March 1, 1999/Revised July 17, 2000

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ID="*" Research supported in part by the NSF Grant No. DMS–9803239. The author greatly enjoyed the hospitality of CIMAT, Gto, Mexico, where part of this work was done.

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Houdré, C. Mixed and Isoperimetric Estimates on the Log-Sobolev Constants of Graphs and Markov Chains. Combinatorica 21, 489–513 (2001). https://doi.org/10.1007/s004930100010

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  • AMS Subject Classification (2000) Classes:  05C99, 60J10, 68R10