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

Fingerprint

Conformal Invariance
invariance
Spacing
spacing
Scaling Limit
Triangular Lattice
Fractal Dimension
fractals
Monte Carlo Simulation
boundary conditions
Boundary conditions
scaling
Curve
Invariant
curves
simulation

Keywords

  • Loop-erased
  • Percolation
  • SLE

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Conformal Invariance of the Loop-Erased Percolation Explorer. / Kennedy, Thomas G.

In: Journal of Statistical Physics, 01.01.2019.

Research output: Contribution to journalArticle

@article{c6a6dc2a2a0c40ff93b17f93c53e87a0,
title = "Conformal Invariance of the Loop-Erased Percolation Explorer",
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.",
keywords = "Loop-erased, Percolation, SLE",
author = "Kennedy, {Thomas G}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10955-019-02354-9",
language = "English (US)",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",

}

TY - JOUR

T1 - Conformal Invariance of the Loop-Erased Percolation Explorer

AU - Kennedy, Thomas G

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Loop-erased

KW - Percolation

KW - SLE

UR - http://www.scopus.com/inward/record.url?scp=85069663519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069663519&partnerID=8YFLogxK

U2 - 10.1007/s10955-019-02354-9

DO - 10.1007/s10955-019-02354-9

M3 - Article

AN - SCOPUS:85069663519

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -