Equidistribution and Brownian motion on the Sierpiński gasket
type: Item
instance of: scholarly article
title: Equidistribution and Brownian motion on the Sierpiński gasket
zbMATH Open document ID: 0915.11041
DOI: 10.1007/BF01332824
author: Peter J. Grabner
author: Robert F. Tichy
published in: Monatshefte für Mathematik
publication date: 1999-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/178804
review text: On the Sierpiński gasket \(G\), various concepts of discrepancy of sequences are investigated and estimates are given. Bounds for the discrepancy of sequences on \(G\) and fractal analogies of classic discrepancy bounds for sequences \(\text{ mod } 1\) are established. Mixing properties of Brownian motion on \(G\) yield a law of the iterated logarithm for sample paths with respect to these notions of discrepancy.
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 1145818
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: uniform distribution
zbMATH Keywords: fractals
zbMATH Keywords: diffusion process
zbMATH Keywords: discrepancy
MaRDI profile type: Publication
cites work: Coupling and Harnack inequalities for Sierpiński carpets
cites work: Brownian motion on the Sierpinski gasket
cites work: Q4726347
cites work: Q3995284
cites work: A uniform law of iterated logarithm for Brownian motion on compact Riemannian manifolds
cites work: Visualizing the p-adic Integers
cites work: Statistical mechanics and fractals
cites work: C-uniform distribution on compact metric spaces
cites work: Mellin transforms and asymptotics: Digital sums
cites work: Das Wienersche Maß einer gewissen Menge von Vektorfunktionen. (The Wiener measure on a certain set of vector functions.)
cites work: On a spectral analysis for the Sierpiński gasket.
cites work: Completely q-multiplicative functions: the Mellin transform approach
cites work: Number of Odd Binomial Coefficients
cites work: Über C-Gleichverteilung
cites work: A harmonic calculus on the Sierpinski spaces
cites work: Brownian motion on nested fractals
cites work: Q4003879
cites work: An inequality for differences of distribution functions
cites work: Mixing sequences of random variables and probablistic number theory
cites work: Irregularities of distribution, VII
cites work: On eigenvalue problems for the random walks on the Sierpinski pre- gaskets
cites work: Q5623000
description: scientific article; zbMATH DE number 1145818