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Teor. Veroyatnost. i Primenen., 1993, Volume 38, Issue 2, Pages 331–344 (Mi tvp3942)  

This article is cited in 1 scientific paper (total in 2 paper)

Asymptotic behavior of a two-dimensional random walk with topological constraints

L. B. Koralov, S. K. Nechaev, Ya. G. Sinaia

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: 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, Markov chain, Wiener branching process, statistical weight.

Full text: PDF file (831 kB)

English version:
Theory of Probability and its Applications, 1993, 38:2, 296–306

Bibliographic databases:

Received: 25.09.1991

Citation: L. B. Koralov, S. K. Nechaev, Ya. G. Sinai, “Asymptotic behavior of a two-dimensional random walk with topological constraints”, Teor. Veroyatnost. i Primenen., 38:2 (1993), 331–344; Theory Probab. Appl., 38:2 (1993), 296–306

Citation in format AMSBIB
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\by L.~B.~Koralov, S.~K.~Nechaev, Ya.~G.~Sinai
\paper Asymptotic behavior of a~two-dimensional random walk with topological constraints
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 2
\pages 331--344
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1317982}
\zmath{https://zbmath.org/?q=an:0807.60067}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 2
\pages 296--306
\crossref{https://doi.org/10.1137/1138026}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NY72300007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. O. A. Vasil'ev, S. K. Nechaev, “Topological Correlations in Trivial Knots: New Arguments in Favor of the Representation of a Crumpled Polymer Globule”, Theoret. and Math. Phys., 134:2 (2003), 142–159  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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