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Equidistribution and Brownian motion on the Sierpiński gasket

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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.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Peter J. Grabner & Robert F. Tichy

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  1. Peter J. Grabner
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  2. Robert F. Tichy
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Dedicated to Prof. Edmund Hlawka on the occasion of his 80th birthday

With 2 Figures

The authors are supported by the Austrian Science Foundation project Nr. P10223-PHY and by the Austrian-Italian scientific cooperation program project Nr. 39

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Grabner, P.J., Tichy, R.F. Equidistribution and Brownian motion on the Sierpiński gasket. Monatshefte für Mathematik 125, 147–164 (1998). https://doi.org/10.1007/BF01332824

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