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2008 First-passage competition with different speeds: positive density for both species is impossible
Olivier Garet, Régine Marchand
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Electron. J. Probab. 13: 2118-2159 (2008). DOI: 10.1214/EJP.v13-581


Consider two epidemics whose expansions on $\mathbb{Z}^d$ are governed by two families of passage times that are distinct and stochastically comparable. We prove that when the weak infection survives, the space occupied by the strong one is almost impossible to detect. Particularly, in dimension two, we prove that one species finally occupies a set with full density, while the other one only occupies a set of null density. Furthermore, we observe the same fluctuations with respect to the asymptotic shape as for the weak infection evolving alone. By the way, we extend the Häggström-Pemantle non-coexistence result "except perhaps for a denumerable set" to families of stochastically comparable passage times indexed by a continuous parameter.


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Olivier Garet. Régine Marchand. "First-passage competition with different speeds: positive density for both species is impossible." Electron. J. Probab. 13 2118 - 2159, 2008.


Accepted: 30 November 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60111
MathSciNet: MR2461538
Digital Object Identifier: 10.1214/EJP.v13-581

Primary: 60K35
Secondary: 82B43

Keywords: Coexistence , competition , First-passage percolation , Moderate deviations , Random growth

Vol.13 • 2008
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