The mixing time of the giant component of a random graph |
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Authors: | Itai Benjamini Gady Kozma Nicholas Wormald |
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Institution: | 1. Department of Mathematics, Weizmann Institute, , Rehovot, 76100 Israel;2. School of Mathematical Sciences, Monash University, , Victoria, 3800 Australia |
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Abstract: | We show that the total variation mixing time of the simple random walk on the giant component of supercritical and is . This statement was proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are “decorated expanders” — an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 383–407, 2014 |
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Keywords: | mixing time random walk random graph expander giant component |
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