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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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The Pleasures and Pains of Studying the Two-Type Richardson Model

The Pleasures and Pains of Studying the Two-Type Richardson Model

Chapter:
(p.39) 2 The Pleasures and Pains of Studying the Two-Type Richardson Model
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Maria Deijfen

Olle Häggström

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0002

This chapter provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on a lattice. In its simplest formulation, the Richardson model describes the evolution of a single infectious entity on the lattice, but more recently the dynamics have been extended to comprise two competing growing entities. For this version of the model, the main question is whether there is a positive probability for both entities to simultaneously grow to occupy infinite parts of the lattice, the conjecture being that the answer is yes if and only if the entities have the same intensity. In this paper attention focuses on the two-type model, but the most important results for the one-type version are also described.

Keywords:   Richardson model, first-passage percolation, asymptotic shape, competing growth, coexistence

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