English

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 SLE4_4, called massive SLE4_4, which is conformally covariant and absolutely continuous with respect to chordal SLE4_4. In this paper, we provide a full and rigorous proof of this statement. Moreover, we show that a massive SLE4_4 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}
}