On the range of random walks in random environment (Q1842125)

In the studies of random walk in random environment, two kinds of random environment, symmetric and nonsymmetric, usually appear. The symmetric random walk is closely linked with an electric network, which motivates the usage of network techniques in the random walk context. The paper addresses the asymptotic behaviour of the range of random walk in symmetric random environment. It is proved that the strong law of large numbers for the range of random walk on \(Z^ d\) in some random environments holds if \(d \geq 3\). A weak law of large numbers holds for \(d = 1\).