On the range of reversible random walks on \(Z^ 2\) in a random environment
Asymptotic behaviours of random walk in random environment rely on the independent increment property of the walk on \(Z^ d\), \(d \geq 1\). The paper discusses reversible random walks on \(Z^ d\), whose increments are not independent, and attempts to establish the law of large numbers for the range of these random walks. The main technical tools are hitting times and hitting distributions. The main result refers to the two- dimensional reversible random walk. The reversibility is here an assumption coming from the connection between the electrical network and the reversible random walk. The analysis cannot be extended to an irreversible random walk.
scientific article; zbMATH DE number 757605