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Reinforced Random Walks and Adic Transformations

Author

Listed:
  • Sarah Bailey Frick

    (The Ohio State University)

  • Karl Petersen

    (University of North Carolina)

Abstract

To a given finite graph we associate three kinds of adic, or Bratteli–Vershik, systems: stationary, symbol-count, and reinforced. We give conditions for the natural walk measure to be adic-invariant and identify the ergodic adic-invariant measures for some classes of examples. If the walk measure is adic-invariant, we relate its ergodic decomposition to the vector of limiting edge traversal frequencies. For some particular nonsimple reinforcement schemes, we calculate the density function of the edge traversal frequencies explicitly.

Suggested Citation

  • Sarah Bailey Frick & Karl Petersen, 2010. "Reinforced Random Walks and Adic Transformations," Journal of Theoretical Probability, Springer, vol. 23(3), pages 920-943, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-010-0282-y
    DOI: 10.1007/s10959-010-0282-y
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