A natural parametrization for the Schramm-Loewner evolution
type: Item
instance of: scholarly article
title: A natural parametrization for the Schramm-Loewner evolution
zbMATH Open document ID: 1234.60087
DOI: 10.1214/10-AOP560
author: Gregory F. Lawler
author: Scott Sheffield
published in: The Annals of Probability
publication date: 2011-12-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/0906.3804
review text: The Schramm-Loewner evolution (SLE) is a model which has been proposed to picture the conformal invariance in the scaling limit of some measures on paths, or clusters on planar lattices, which occur in statistical mechanics. The main purpose of the paper is to propose a Markovian parametrization for this SLE, and to this end the authors derive a Doob-Meyer decomposition for submartingales satisfying a second moment bound. This unique parametrization is referred to as natural to emphasize the analogy with the natural parametrization of smooth curves and the main results are stated in terms of martingales and asymptotic limits.
Mathematics Subject Classification ID: 60J67
zbMATH DE Number: 5987673
zbMATH Keywords: Schramm-Loewner evolution
zbMATH Keywords: natural parametrization
reviewed by: Guy Jumarie
MaRDI profile type: Publication
arXiv ID: 0906.3804
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OpenAlex ID: W2349285619
description: scientific article