Reinforced Random Walks and Adic Transformations

Sarah Bailey Frick () and Karl Petersen ()
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Sarah Bailey Frick: The Ohio State University
Karl Petersen: University of North Carolina

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 920-943

Abstract: 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.

Keywords: Reinforced random walks; Adic transformations; Invariant measures; Eulerian numbers; Ergodic transformations; Bratteli diagrams; 37A30; 37A05 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-010-0282-y

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