New York Journal of Mathematics
Volume 5 (1999) 107-113


Russell Lyons and Oded Schramm

Stationary Measures for Random Walks in a Random Environment with Random Scenery

Published: July 29, 1999
Keywords: Cayley graph, group, transitive
Subject: Primary 60B99, 60J15. Secondary 28D15.

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.


First Author: Research partially supported by NSF grant DMS-9802663
Second Author: The Sam and Ayala Zacks Professorial Chair

Author information

Russell Lyons:
Department of Mathematics, Indiana University, Bloomington, IN 47405-5701, USA

Oded Schramm:
Mathematics Department, The Weizmann Institute of Science, Rehovot 76100, Israel