Strong path convergence from Loewner driving function convergence
type: Item
instance of: scholarly article
title: Strong path convergence from Loewner driving function convergence
zbMATH Open document ID: 1255.60148
DOI: 10.1214/10-AOP627
author: Scott Sheffield
author: Nike Sun
published in: The Annals of Probability
publication date: 2012-05-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1003.4675
full work available at URL: https://projecteuclid.org/euclid.aop/1332772714
review text: The Loewner differential equation, provided by Loewner in 1923, relates a planar self-avoiding curve to a real-valued continuous function (the ``Loewner driving function'') via conformal mappings. The authors introduce ``uniform convergence'' as a short-hand for ``convergence in law'' with respect to the uniform metric, when speaking of random curves. The goal of the present article is to provide a more general criterion for deducing uniform convergence, which is less dependent on specific features of the model at hand.
reviewed by: Sophia L. Kalpazidou
Mathematics Subject Classification ID: 60J67
Mathematics Subject Classification ID: 30C35
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 6032937
zbMATH Keywords: strong path-convergence
zbMATH Keywords: Loewner driving convergence
MaRDI profile type: Publication
arXiv ID: 1003.4675
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OpenAlex ID: W2032595936
description: scientific article; zbMATH DE number 6032937