Walks in rigid environments

We consider a motion of the particle in a random configuration of scatterer s on a lattice. There is a feedback of the particle on an environment which is characterized by its rigidity r. The type of a scatterer at a site of t he lattice changes after the rth visit of the particle to this site. We sho w that in one-dimensional lattice the particle will eventually propagate in one direction with a random velocity if a rigidity is an odd number and it will oscillate (about origin) with an unbounded amplitude if r is an even number. The average velocity of propagation and the expected time until the first passage through a given site of the lattice are computed. (C) 2000 E lsevier Science B.V. All rights reserved.