Law of the SLE tip
Probability
2023-11-17 v3
Abstract
We analyze the law of the SLE tip at a fixed time in capacity parametrization. We describe it as the stationary law of a suitable diffusion process, and show that it has a density which is a unique solution of a certain PDE. Moreover, we identify the phases in which the even negative moments of the imaginary value are finite. For the negative second and negative fourth moments we provide closed-form expressions.
Keywords
Cite
@article{arxiv.2110.11247,
title = {Law of the SLE tip},
author = {Oleg Butkovsky and Vlad Margarint and Yizheng Yuan},
journal= {arXiv preprint arXiv:2110.11247},
year = {2023}
}