A non-intersecting random walk on the Manhattan lattice and SLE6

Tom Kennedy

A non-intersecting random walk on the Manhattan lattice and SLE₆

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces for bond percolation on a square lattice. So it is natural to conjecture that the scaling limit is SLE₆. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.

MSC Codes 60J67, 60G50, 60K35, 82B41, 82B43

Original language	English (US)
Journal	Unknown Journal
State	Published - Mar 18 2018

ASJC Scopus subject areas

General

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title = "A non-intersecting random walk on the Manhattan lattice and SLE6",

abstract = "We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces for bond percolation on a square lattice. So it is natural to conjecture that the scaling limit is SLE6. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.MSC Codes 60J67, 60G50, 60K35, 82B41, 82B43",

author = "Tom Kennedy",

year = "2018",

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N2 - We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces for bond percolation on a square lattice. So it is natural to conjecture that the scaling limit is SLE6. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.MSC Codes 60J67, 60G50, 60K35, 82B41, 82B43

AB - We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces for bond percolation on a square lattice. So it is natural to conjecture that the scaling limit is SLE6. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.MSC Codes 60J67, 60G50, 60K35, 82B41, 82B43

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