Area distribution of the planar random loop boundary

TL;DR

This paper uses Monte Carlo simulations to study the area distribution of the outer boundary of planar random loops on different lattices, suggesting the Airy distribution as the underlying limit distribution, similar to self-avoiding loops.

Contribution

It provides numerical evidence that the area distribution of planar random loop boundaries follows the Airy distribution, extending understanding of geometric properties of random loops.

Findings

The area distribution fits the Airy distribution.

The results are consistent across square and triangular lattices.

Supports the universality of the Airy distribution in loop models.

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.