ASYMPTOTIC-BEHAVIOR OF A 2-DIMENSIONAL RANDOM-WALK WITH TOPOLOGICAL CONSTRAINTS

A set of topologically trivial closed random walks on the plane is discussed, i.e., the walks that can be contracted to points and remain on the lattice during deformation. As the walk length tends to infinity, the limiting finite-dimensional distributions can be found for normalized coordinates, which can be described in terms of the Wiener branching process.