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Mixing of the upper triangular matrix walk
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  • Published: 06 July 2012

Mixing of the upper triangular matrix walk

  • Yuval Peres1 &
  • Allan Sly2 

Probability Theory and Related Fields volume 156, pages 581–591 (2013)Cite this article

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  • 10 Citations

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Abstract

We study a natural random walk over the upper triangular matrices, with entries in the field \({\mathbb{Z}_2}\) , generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n 2) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields \({\mathbb{Z}_q}\) for q prime.

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Author information

Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98052-6399, USA

    Yuval Peres

  2. Berkeley Department of Statistics, University of California, 367 Evans Hall, Berkeley, CA, 94720, USA

    Allan Sly

Authors
  1. Yuval Peres
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  2. Allan Sly
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Corresponding author

Correspondence to Allan Sly.

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Cite this article

Peres, Y., Sly, A. Mixing of the upper triangular matrix walk. Probab. Theory Relat. Fields 156, 581–591 (2013). https://doi.org/10.1007/s00440-012-0436-1

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  • Received: 23 May 2011

  • Revised: 13 May 2012

  • Published: 06 July 2012

  • Issue Date: August 2013

  • DOI: https://doi.org/10.1007/s00440-012-0436-1

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Keywords

  • Mixing time
  • Random walks on groups

Mathematics Subject Classification

  • 60J10
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