Multiple SLE and the complex Burgers equation
Complex Variables
2015-06-19 v1 Mathematical Physics
math.MP
Probability
Abstract
In this paper we ask whether one can take the limit of multiple SLE as the number of slits goes to infinity. In the special case of slits that connect points of the boundary to one fixed point, one can take the limit of the Loewner equation that describes the growth of those slits in a simultaneous way. In this case, the limit is a deterministic Loewner equation whose vector field is determined by a complex Burgers equation.
Cite
@article{arxiv.1506.04679,
title = {Multiple SLE and the complex Burgers equation},
author = {Andrea del Monaco and Sebastian Schleissinger},
journal= {arXiv preprint arXiv:1506.04679},
year = {2015}
}