Vertex and edge expansion properties for rapid mixing

  • Authors:

  • Ravi Montenegro

  • Affiliations:

  • School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

  • Venue:
  • Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
  • Year:
  • 2005

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Abstract

We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is then used to give an isoperimetric proof that a random walk on the grid [k]n mixes in time O*(k2n). © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005