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The Average Displacement of the Simple Random Walk on the Sierpiński Graph

Published online by Cambridge University Press:  17 March 2003

ELMAR TEUFL
ELMAR TEUFL
Affiliation:
Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria (e-mail: teufl@finanz.math.tu-graz.ac.at)
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Abstract

We investigate the asymptotic behaviour of the average displacement of the simple random walk on the Sierpiński graph. The existence of an oscillating factor in this asymptotics is shown rigorously. The proof depends mainly on the analysis of the corresponding generating function. Using a functional equation and techniques from complex analysis we obtain the desired properties of this generating function.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 2 , March 2003 , pp. 203 - 222
Copyright
2003 Cambridge University Press

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