Geodesic
Asymptotic behavior of a~two-dimensional random walk with topological constraints
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 331-344

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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.
Keywords: random walk, limiting distribution, Cayley tree, Wiener branching process, statistical weight.
Mots-clés : Markov chain 
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     author = {L. B. Koralov and S. K. Nechaev and Ya. G. Sinai},
     title = {Asymptotic behavior of a~two-dimensional random walk with topological constraints},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {331--344},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a6/}
}
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L. B. Koralov; S. K. Nechaev; Ya. G. Sinai. Asymptotic behavior of a~two-dimensional random walk with topological constraints. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 331-344. http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a6/