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Russell Lyons and Oded Schramm
Stationary Measures for Random Walks in a Random Environment with Random Scenery
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| Published: |
July 29, 1999 |
| Keywords: |
Cayley graph, group, transitive |
| Subject: |
Primary 60B99, 60J15. Secondary 28D15. |
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Abstract
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.
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| Acknowledgements
First Author: Research partially supported by NSF grant DMS-9802663
Second Author: The Sam and Ayala Zacks Professorial Chair
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| Author information
Russell Lyons:
Department of Mathematics, Indiana University, Bloomington, IN 47405-5701, USA
rdlyons@indiana.edu
http://php.indiana.edu/~rdlyons/
Oded Schramm:
Mathematics Department, The Weizmann Institute of Science, Rehovot 76100, Israel
schramm@wisdom.weizmann.ac.il
http://www.wisdom.weizmann.ac.il/~schramm/
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