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Branching and tree indexed random walks on fractals

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

András Telcs  and
Nicholas C. Wormald
András Telcs*
Affiliation:
International Business School, Budapest
Nicholas C. Wormald*
Affiliation:
University of Melbourne
*
∗Postal address: Head of Library and Computing, International Business School, Tarogato u. 2–4, 1021 Budapest, Hungary. Partial support from OTKA T 016237 and the Australian Research Council.
∗∗Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3052, Australia. Email address: [email protected].
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Abstract

This paper deals with the recurrence of branching random walks on polynomially growing graphs. Amongst other things, we demonstrate the strong recurrence of tree indexed random walks determined by the resistance properties of spherically symmetric graphs. Several branching walk models are considered to show how the branching mechanism influences the recurrence behaviour.

Keywords

Branching processrandom walkbranching random walkfractal

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 999 - 1011
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Supported by the Australian Research Council.

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