### Abstract

The joint limiting probability distribution is studied for the two-dimensional random walk with topological constraints, ω(2ns), on ℤ^{2} lattice, where 2n is its total length and (0≤s≤1). The expression for the density of finite-dimensional limiting probability distribution π{ξ_{n}(s_{1}),ξ_{n}(s _{2}),...,ξ_{n}(s) = ω(2ns)/n^{1/4} is described.

Original language | English (US) |
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Pages (from-to) | 131-133 |

Number of pages | 3 |

Journal | Chaos |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

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## Cite this

Koralov, L. B., Nechaev, S. K., & Sinai, Y. G. (1991). Limiting probability distribution for a random walk with topological constraints.

*Chaos*,*1*(2), 131-133. https://doi.org/10.1063/1.165821