Stationary measures for random walks in a random environment with random scenery

  • Russell Lyons ,
  • Oded Schramm

New York Journal of Mathematics | , Vol 5: pp. 107-113

Let Γ act on a countable set V with only finitely many orbits. Given a Γ-invariant random environment for a Markov chain on V and a random scenery, we exhibit, under certain conditions, an equivalent stationary measure for the environment and scenery from the viewpoint of the random walker. Such theorems have been very useful in investigations of percolation on quasi-transitive graphs.