Simulating self-avoiding walks in bounded domains

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5 Scopus citations


Let D be a domain in the plane containing the origin. We are interested in the ensemble of self-avoiding walks (SAWs) in D which start at the origin and end on the boundary of the domain. We introduce an ensemble of SAWs that we expect to have the same scaling limit. The advantage of our ensemble is that it can be simulated using the pivot algorithm. Our ensemble makes it possible to accurately study Schramm-Loewner evolution (SLE) predictions for the SAW in bounded simply connected domains. One such prediction is the distribution along the boundary of the endpoint of the SAW. We use the pivot algorithm to simulate our ensemble and study this density. In particular the lattice effects in this density that persist in the scaling limit are seen to be given by a purely local function.

Original languageEnglish (US)
Article number095219
JournalJournal of Mathematical Physics
Issue number9
StatePublished - Sep 28 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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