INFINITE PATHS ON A RANDOM ENVIRONMENT OF Z^2 WITH BOUNDED AND RECURRENT SUMS
This paper considers a random structure on the lattice Z
2 of the following
kind. To each edge e a random variable Xe is assigned, together with a random sign
Y_e ∈ {−1, +1}. For an infinite self-avoiding path on Z
2
starting at the origin consider the
sequence of partial sums along the path. These are computed by summing the Xe’s for
the edges e crossed by the path, with a sign depending on the direction of the crossing.
If the edge is crossed rightward or upward the sign is given by Ye, otherwise by −Ye. We