Massive SLE$_4$ and the scaling limit of the massive harmonic explorer
Probability
2023-07-24 v1 Mathematical Physics
math.MP
Abstract
The massive harmonic explorer is a model of random discrete path on the hexagonal lattice that was proposed by Makarov and Smirnov as a massive perturbation of the harmonic explorer. They argued that the scaling limit of the massive harmonic explorer in a bounded domain is a massive version of chordal SLE, called massive SLE, which is conformally covariant and absolutely continuous with respect to chordal SLE. In this paper, we provide a full and rigorous proof of this statement. Moreover, we show that a massive SLE curve can be coupled with a massive Gaussian free field as its level line, when the field has appropriate boundary conditions.
Keywords
Cite
@article{arxiv.2307.11509,
title = {Massive SLE$_4$ and the scaling limit of the massive harmonic explorer},
author = {Léonie Papon},
journal= {arXiv preprint arXiv:2307.11509},
year = {2023}
}