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In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusExistence and Coexistence in First-Passage Percolation

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Existence and Coexistence in... [We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for the multi-type Richardson model. In two dimensions this establishes a dual relation between the existence of infinite geodesics and coexistence among competing types. The argument amounts to making precise the heuristic that infinite geodesics can be thought of as ‘highways to infinity’. We explain the limitations of the current techniques by presenting a partial result in dimensions d > 2.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusExistence and Coexistence in First-Passage Percolation

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.

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References (33)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
1 –15
DOI
10.1007/978-3-030-60754-8_1
Publisher site
See Chapter on Publisher Site

Abstract

[We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for the multi-type Richardson model. In two dimensions this establishes a dual relation between the existence of infinite geodesics and coexistence among competing types. The argument amounts to making precise the heuristic that infinite geodesics can be thought of as ‘highways to infinity’. We explain the limitations of the current techniques by presenting a partial result in dimensions d > 2.]

Published: Nov 4, 2020

Keywords: First-passage percolation; Competing growth; Geodesics; Busemann functions

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