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Asymptotic behavior of a two-dimensional random walk with topological constraints. (English. Russian original) Zbl 0807.60067

Theory Probab. Appl. 38, No. 2, 296-306 (1993); translation from Teor. Veroyatn. Primen. 38, No. 2, 331-344 (1993).
Summary: 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.

MSC:

60G50 Sums of independent random variables; random walks