Area distribution of the planar random loop boundary

Abstract

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.

10 pages, 2 figures. v2: minor changes, version as published

References in corpus (8)

• Random planar curves and Schramm-Loewner evolutions
• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• Conformal Invariance and Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk - Monte Carlo Tests
• Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk
• Scaling behaviour of two-dimensional polygon models
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
• Scaling function for self-avoiding polygons

Cited by in corpus (9)

• Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
• Conformal Random Geometry
• Functionals of the Brownian motion, localization and metric graphs
• The first-passage area for drifted Brownian motion and the moments of the Airy distribution
• The expected area of the filled planar Brownian loop is Pi/5
• Critical behavior in topological ensembles
• Scaling prediction for self-avoiding polygons revisited
• Convex hull of n planar Brownian paths: an exact formula for the average number of edges
• Some remarks on SLE bubbles and Schramm's two-point observable