Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle''
type: Item
instance of: scholarly article
title: Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle''
zbMATH Open document ID: 1023.60051
DOI: 10.1016/S0022-1236(02)00011-3
published in: Journal of Functional Analysis
publication date: 2003-03-26T00:00:00Z
review text: The Brownian motion \((g_t)\) on the group of \(C^\infty\)-diffeomorphisms on \(\mathbb{S}^1\), equipped with the so-called \(H^{3/2}\) metric, presents a decrease of regularity as time \(t\) goes by. The aim of this work is to supply a lower bound for the remaining Hölder regularity at time \(t>0\). So the main result asserts that the law of \(g_t\) is carried by \(\alpha\)-Hölder diffeomorphisms, for all \(\alpha<(1-\sqrt{1-e^{-t/2}}) /(1+\sqrt{1-e^{-t/2}})\). The method uses a study of the two-points process \((g_t(\theta), g_t(\theta'))\), showing in particular that no confluence takes place.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 58D20
Mathematics Subject Classification ID: 46N50
zbMATH DE Number: 1888375
zbMATH Keywords: diffeomorphisms of the circle
zbMATH Keywords: Brownian motion
zbMATH Keywords: Hölder continuity
author: Hélène Airault
author: Jiagang Ren
MaRDI profile type: Publication
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full work available at URL: s0022-1236(02)00011-3
OpenAlex ID: W1996447039
description: scientific article; zbMATH DE number 1888375