# Systemes de particules multicolores

Abstract : Most mathematical models in the biological literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations obtained under global dispersion assumptions, thus leaving out any spatial structure. Interacting particle systems are Markov processes with state space $F^S$ where $F$ is a finite set of colors and where $S$ is a spatial structure, typically $\Z^d$. They are ideally suited to study the consequences of the inclusion of a spatial structure in the form of local interactions. We investigate the mathematical properties (stationary distribution, geometry of the configurations, phase transitions) of various multicolor particle systems defined on $\Z^d$. Each of these systems is intended to model local interactions within a spatially structured community of populations. More precisely, the biological processes we investigate are ecological succession, allelopathy or competition between an inhibitory species and a susceptible species, multi-species host-symbiont interactions, and persistent gene flow from transgenic crops to wild relatives through pollination in a heterogeneous environment. The mathematical techniques are probabilistic, including coupling, duality, multiscale arguments, oriented percolation, asymptotic properties of random walks, and large deviations estimates.
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Cited literature [127 references]

https://tel.archives-ouvertes.fr/tel-00164594
Contributor : Nicolas Lanchier <>
Submitted on : Friday, July 20, 2007 - 9:24:46 PM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
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• HAL Id : tel-00164594, version 1

### Citation

Nicolas Lanchier. Systemes de particules multicolores. Mathématiques [math]. Université de Rouen, 2005. Français. ⟨tel-00164594⟩

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