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Chutes and Ladders in Markov Chains

Author

Listed:
  • Persi Diaconis

    (Stanford University)

  • Rick Durrett

    (Cornell University)

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.

Suggested Citation

  • Persi Diaconis & Rick Durrett, 2001. "Chutes and Ladders in Markov Chains," Journal of Theoretical Probability, Springer, vol. 14(3), pages 899-926, July.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:3:d:10.1023_a:1017509611178
    DOI: 10.1023/A:1017509611178
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