Random walk on upper triangular matrices mixes rapidly |
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Authors: | Don Coppersmith Igor Pak |
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Institution: | (1) T.J. Watson Research Center, IBM, Yorktown Heights, NY 10598, USA. e-mail: copper@watson.ibm.com, US;(2) Department of Mathematics, Yale University, New Haven, CT 06520, USA e-mail: paki@math.yale.edu, US |
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Abstract: | We present an upper bound O(n
2
) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant,
and find tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion
process on a circle indeed mixes more rapidly than the corresponding symmetric process.
Received: 25 January 1999 / Revised version: 17 September 1999 / Published online: 14 June 2000 |
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Keywords: | Mathematics Subject Classification (1991): 60J10 |
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