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Multitype shape theorems for first passage percolation models

Part of: Equilibrium statistical mechanics Geometric probability and stochastic geometry Special processes

Published online by Cambridge University Press:  01 July 2016

Leandro P. R. Pimentel
Leandro P. R. Pimentel*
Affiliation:
École Polytechnique Fédérale de Lausanne
*
∗ Postal address: Institut de Mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland. Email address: leandro.pimentel@epfl.ch
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Abstract

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A Euclidean first passage percolation model describing the competing growth between k different types of infection is considered. We focus on the long-time behavior of this multitype growth process and we derive multitype shape results related to its morphology.

Keywords

First passage percolationcompeting growthmultitype shape theoremcompetition interface

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 1 , March 2007 , pp. 53 - 76
Copyright
Copyright © Applied Probability Trust 2007 

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