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The Cutoff Phenomenon in Finite Markov Chains
Proceedings of the National Academy of Sciences of the United States of America
Vol. 93, No. 4 (Feb. 20, 1996), pp. 1659-1664
Published by: National Academy of Sciences
Stable URL: http://www.jstor.org/stable/38640
Page Count: 6
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Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists.
Proceedings of the National Academy of Sciences of the United States of America © 1996 National Academy of Sciences