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
Mots-clés : Markov chain
@article{TVP_1993_38_2_a6,
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},
year = {1993},
volume = {38},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a6/}
}
TY - JOUR AU - L. B. Koralov AU - S. K. Nechaev AU - Ya. G. Sinai TI - Asymptotic behavior of a two-dimensional random walk with topological constraints JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1993 SP - 331 EP - 344 VL - 38 IS - 2 UR - http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a6/ LA - ru ID - TVP_1993_38_2_a6 ER -
%0 Journal Article %A L. B. Koralov %A S. K. Nechaev %A Ya. G. Sinai %T Asymptotic behavior of a two-dimensional random walk with topological constraints %J Teoriâ veroâtnostej i ee primeneniâ %D 1993 %P 331-344 %V 38 %N 2 %U http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a6/ %G ru %F TVP_1993_38_2_a6
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/