Conformal welding of independent Gaussian multiplicative chaos measures
Probability
2026-01-27 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the boundary of the unit disk we show that there exist conformal maps to complementary domains on the Riemann sphere such that the pushforward of the normalised measures agree on their common boundary.
Keywords
Cite
@article{arxiv.2305.18062,
title = {Conformal welding of independent Gaussian multiplicative chaos measures},
author = {Antti Kupiainen and Michael McAuley and Eero Saksman},
journal= {arXiv preprint arXiv:2305.18062},
year = {2026}
}
Comments
To appear in Journal of the European Mathematical Society