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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 24, Fasc. 1,
pages 121 - 144
 

THE EXISTENCE OF A STEADY STATE FOR A PERTURBED SYMMETRIC RANDOM WALK ON A RANDOM LATTICE

T. Komorowski
G. Krupa

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 m
 a  for the environment process (z(t))
     t>0  corresponding to the walk. This steady state has the property that the ergodic averages of (F (z(t)))   ,
        t>0 where F is local (i.e. it depends on finitely many bonds of the lattice only), converge almost surely in the annealed measure to  integral 
 F dma.

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.

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