A Non-intersecting Random Walk on the Manhattan Lattice and SLE 6

Tom Kennedy

doi:10.1007/s10955-018-2176-9

A Non-intersecting Random Walk on the Manhattan Lattice and SLE ₆

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 SLE ₆. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.

Original language	English (US)
Pages (from-to)	77-96
Number of pages	20
Journal	Journal of Statistical Physics
Volume	174
Issue number	1
DOIs	https://doi.org/10.1007/s10955-018-2176-9
State	Published - Jan 15 2019

Keywords

Bond percolation
Manhattan lattice
Non-intersecting random walk
Schramm–Loewner evolution

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s10955-018-2176-9

Cite this

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title = "A Non-intersecting Random Walk on the Manhattan Lattice and SLE 6",

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 SLE 6. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.",

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