Self-repelling walk on the Sierpiński gasket
type: Item
instance of: scholarly article
title: Self-repelling walk on the Sierpiński gasket
zbMATH Open document ID: 1017.60101
author: Kumiko Hattori
author: Tetsuya Hattori
author: Ben M. Hambly
publication date: 2002-12-01T00:00:00Z
review text: The authors study a family, parametrized by \(u \in [0,1]\), of self-repelling processes constructed by taking continuum limits of the sequences of random walks on the graph approximations to the (finite) Sierpiński gasket. The self-similar processes corresponding to \(u \in (0,1)\) interpolate between the self-avoiding process (case \(u=0\)) and the Brownian motion (\(u=1\)), so that the path measure \(P^u\) is weakly continuous in \(u\) and the order of the Hölder continuity of the sample path is also continuous in the parameter. In contrast to some previous models, that originated in the studies of polymers, the parameter does not directly count the number of returns of the walks to bonds or sites. This new construction can produce different interpolating families of self-similar processes on \(\mathbb{R}\) when applied to random walks on \(\mathbb{Z}\). Moreover, a law of the iterated logarithm is established for thus arising processes via the large deviations estimates for the supercritical branching process describing the path.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1837437
zbMATH Keywords: self-repelling processes
zbMATH Keywords: Sierpiński gasket
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
full work available at URL: s004400100192
OpenAlex ID: W1990964765
DOI: 10.1007/S004400100192
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1837437