Uniqueness of the mixing measure for a random walk in a random environment on the positive integers

Maren Eckhoff (Technical University of Munich)
Silke W.W. Rolles (Technical University of Munich)

Abstract


Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An application to linearly edge-reinforced random walk is given.

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Pages: 31-35

Publication Date: February 3, 2009

DOI: 10.1214/ECP.v14-1441

References

  1. F.Merkl and S.W.W. Rolles. A random environment for linearly edge-reinforced random walks on infinite graphs. Prob. Th. Rel. Fields 138 (2007), 157-176. Math. Review 2008j:60235
  2. R.Pemantle. Phase transition in reinforced random walk and RWRE on trees. Ann. Probab. 16 (1988), 1229-1241. Math. Review 89g:60220
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