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Random walk on upper triangular matrices mixes rapidly
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  • Published: July 2000

Random walk on upper triangular matrices mixes rapidly

  • Don Coppersmith1 &
  • Igor Pak2 

Probability Theory and Related Fields volume 117, pages 407–417 (2000)Cite this article

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  • 5 Citations

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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.

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Authors and Affiliations

  1. T.J. Watson Research Center, IBM, Yorktown Heights, NY 10598, USA. e-mail: copper@watson.ibm.com, , , , , , US

    Don Coppersmith

  2. Department of Mathematics, Yale University, New Haven, CT 06520, USA e-mail: paki@math.yale.edu, , , , , , US

    Igor Pak

Authors
  1. Don Coppersmith
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  2. Igor Pak
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Additional information

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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  • Issue Date: July 2000

  • DOI: https://doi.org/10.1007/s004400050012

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  • Mathematics Subject Classification (1991): 60J10
  • Key words and phrases: Random walks on groups – Strong stationary time – Separation distance – Upper triangular matrices – Asymmetric exclusion process
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