THE EXISTENCE OF A STEADY STATE FOR A PERTURBED
SYMMETRIC RANDOM WALK ON A RANDOM LATTICE
Abstract: In the present paper we consider a continuous time random walk on an anisotropic
random lattice. We show the existence of a steady state for the environment process
corresponding to the walk. This steady state has the property that the ergodic
averages of where is local (i.e. it depends on finitely many bonds of
the lattice only), converge almost surely in the annealed measure to
2000 AMS Mathematics Subject Classification: Primary 60F17, 35B27; Secondary
60G44.
Key words and phrases: Random field, passive tracer, random walk in random
environment, Einstein relation.