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Random systems in ultrametric spaces

Part of: Combinatorial probability Graph theory Special processes

Published online by Cambridge University Press:  01 February 2019

D. A. Dawson  and
L. G. Gorostiza
D. A. Dawson*
Affiliation:
Carleton University
L. G. Gorostiza*
Affiliation:
CINVESTAV
*
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
Department of Mathematics, CINVESTAV-IPN, Apartado Postal 14-740, Mexico DF 07000, Mexico. Email address: lgorosti@math.cinvestav.mx
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Abstract

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We discuss percolation and random walks in a class of homogeneous ultrametric spaces together with similarities and differences in ultrametric and Euclidean spaces. We briefly outline the role of these models in the study of interacting systems. Several open problems are presented.

Keywords

Ultrametric spacehierarchical latticerandom graphpercolationrandom walkinteracting systembranching

MSC classification

Primary: 05C80: Random graphs 05C81: Random walks on graphs 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60C05: Combinatorial probability
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 83 - 97
Copyright
Copyright © Applied Probability Trust 2018 

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