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Rates of convergence of random walk on distance regular graphs
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  • Published: December 1998

Rates of convergence of random walk on distance regular graphs

  • Eric David Belsley1 

Probability Theory and Related Fields volume 112, pages 493–533 (1998)Cite this article

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  • 8 Citations

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Abstract.

When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and that a sharp cutoff phenomenon occurs. For most examples, we determine the set on which the variation distance is achieved, and the precise rate at which it decays.

The upper bound argument uses spectral methods – combining the usual Cauchy-Schwarz bound on variation distance with a bound on the tail probability of a first-hitting time, derived from its generating function.

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Authors and Affiliations

  1. Department of Mathematics, 515 Ungar Building, University of Miami, Coral Gables, FL 33146-4250, USA (email: belsley@math.miami.edu), , , , , , US

    Eric David Belsley

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  1. Eric David Belsley
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Received: 2 April 1997 / Revised version: 10 May 1998

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Belsley, E. Rates of convergence of random walk on distance regular graphs. Probab Theory Relat Fields 112, 493–533 (1998). https://doi.org/10.1007/s004400050198

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  • Issue Date: December 1998

  • DOI: https://doi.org/10.1007/s004400050198

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  • Mathematics Subject Classification (1991): 60B15
  • 60J10
  • 60J15
  • 05C50
  • 0FE30
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