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

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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 languageEnglish (US)
Pages (from-to)77-96
Number of pages20
JournalJournal of Statistical Physics
Volume174
Issue number1
DOIs
StatePublished - 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

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