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Journal of Theoretical Probability

, Volume 14, Issue 3, pp 899–926 | Cite as

Chutes and Ladders in Markov Chains

  • Persi Diaconis
  • Rick Durrett
Article

Abstract

We investigate how the stationary distribution of a Markov chain changes when transitions from a single state are modified. In particular, adding a single directed edge to nearest neighbor random walk on a finite discrete torus in dimensions one, two, or three changes the stationary distribution linearly, logarithmically, or only locally. Related results are derived for birth and death chains approximating Bessel diffusions and for random walk on the Sierpinski gasket.

Markov chains stationary distribution Bessel diffusions Sierspinski gasket 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Persi Diaconis
    • 1
  • Rick Durrett
    • 2
  1. 1.Department of StatisticsStanford UniversityStanford
  2. 2.Department of MathematicsCornell UniversityIthaca

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