Conformal Invariance of the Loop-Erased Percolation Explorer

Research output: Contribution to journalArticle

Abstract

We consider critical percolation on the triangular lattice in a bounded simply connected domain with boundary conditions that force an interface between two prescribed boundary points. We say the interface forms a “near-loop” when it comes within one lattice spacing of itself. We define a new curve by erasing these near-loops as we traverse the interface. Our Monte Carlo simulations of this model lead us to conclude that the scaling limit of this loop-erased percolation interface is conformally invariant and has fractal dimension 4 / 3. However, it is not SLE 8 / 3. We also consider the process in which a near-loop is when the explorer comes within two lattice spacings of itself.

Original languageEnglish (US)
JournalJournal of Statistical Physics
DOIs
StatePublished - Jan 1 2019

Keywords

  • Loop-erased
  • Percolation
  • SLE

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Conformal Invariance of the Loop-Erased Percolation Explorer'. Together they form a unique fingerprint.

  • Cite this