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.
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Received: 25 January 1999 / Revised version: 17 September 1999 / Published online: 14 June 2000
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Coppersmith, D., Pak, I. Random walk on upper triangular matrices mixes rapidly. Probab Theory Relat Fields 117, 407–417 (2000). https://doi.org/10.1007/s004400050012
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DOI: https://doi.org/10.1007/s004400050012
- Mathematics Subject Classification (1991): 60J10
- Key words and phrases: Random walks on groups – Strong stationary time – Separation distance – Upper triangular matrices – Asymmetric exclusion process