Equidistribution and Brownian motion on the Sierpiński gasket

Peter J. Grabner*, Robert F. Tichy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce several concepts of discrepancy for sequences on the Sierpiński gasket. Furthermore a law of iterated logarithm for the discrepancy of trajectories of Brownian motion is proved. The main tools for this result are regularity properties of the heat kernel on the Sierpiński gasket. Some of the results can be generalized to arbitrary nested fractals in the sense of T. Lindstrøm.

Original languageEnglish
Pages (from-to)147-164
Number of pages18
JournalMonatshefte fur Mathematik
Volume125
Issue number2
DOIs
Publication statusPublished - 1 Jan 1998

Keywords

  • Diffusion processes
  • Discrepancy
  • Fractals
  • Uniform distribution

ASJC Scopus subject areas

  • Mathematics(all)

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