On the Hitting Point Distribution for Random Walks in Bounded Domains

The report examines the classical problem of the hitting point distribution for a random walk entering a set within a two-dimensional lattice strip. The limit of this distribution is investigated as the starting point of the walk is moved far from the boundary. In the second part of the report, the obtained results are used to calculate the rate of particle accumulation on the boundary and in the problem of the growth rate of a cluster formed by the accumulated particles.