## REINFORCED RANDOM WALKS AND ADIC TRANSFORMATIONS

by
Sarah Bailey
,
Frick
,
Karl Petersen

### BibTeX

@MISC{Bailey_reinforcedrandom,

author = {Sarah Bailey and Frick and Karl Petersen},

title = {REINFORCED RANDOM WALKS AND ADIC TRANSFORMATIONS},

year = {}

}

### OpenURL

### 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 adicinvariant measures for some classes of examples. If the walk measure is adicinvariant 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. 1.