Uniqueness of the mixing measure for a random walk in a random environment on the positive integers. (English) Zbl 1189.60189

Eckhoff, Maren; Rolles, Silke W. W.

Electron. Commun. Probab. 14, 31-35 (2009).

Summary: 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.

MSC:

60K37	Processes in random environments
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

random walk in a random environment; mixing measure