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| DOI | 10.5802/JEP.132 | ||||
| Año | 2020 | ||||
| Tipo | artículo de investigación |
Citas Totales
Autores Afiliación Chile
Instituciones Chile
% Participación
Internacional
Autores
Afiliación Extranjera
Instituciones
Extranjeras
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by K and in the limit K → +∞, the realizations of such processes get close, in any fixed finite-time window, to the trajectories of a dynamical system whose vector field is defined by the birth and death rates. Assuming this dynamical system has a unique attracting fixed point, we analyzed the behavior of these processes for finite K and finite times, “interpolating" between the two limiting regimes just mentioned. In the present work, we are mainly interested in the following question: Observing a realization of the process, can we determine the so-called engineering resilience? To answer this question, we establish two relations which intermingle the resilience, which is a macroscopic quantity defined for the dynamical system, and the fluctuations of the process, which are microscopic quantities. Analogous relations are well known in nonequilibrium statistical mechanics. To exploit these relations, we need to introduce several estimators which we control for times between log K (time scale to converge to the qsd) and exp(K) (time scale of mean time to extinction).
| Ord. | Autor | Género | Institución - País |
|---|---|---|---|
| 1 | Chazottes, Jean René | Hombre |
Centre de Physique Theorique de l' Ecole Polytechnique - Francia
Ecole Polytech - Francia |
| 2 | Collet, P. | Hombre |
Centre de Physique Theorique de l' Ecole Polytechnique - Francia
Ecole Polytech - Francia |
| 3 | Martinez, Servet | Hombre |
Universidad de Chile - Chile
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| 4 | Meleard, S. | Mujer |
Centre de Mathématiques Appliquées - Francia
Ecole Polytech - Francia |
| Fuente |
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| Basal CONICYT |
| Basal Conicyt CMM |
| Veolia Environnement-École Polytechnique-Museum national d’Histoire naturelle-Fondation X. P. C. |
| Chair "Modelisation Mathematique et Biodiversite" of Veolia Environnement-Ecole Polytechnique-Museum national d'Histoire naturelle-Fondation X. P. C. |
| Agradecimiento |
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| S. M. has been supported by the Chair “Modélisation Mathématique et Biodiversité” of Veolia Environnement-École Polytechnique-Museum national d’Histoire naturelle-Fondation X. P. C. and S. M. warmly thank the Basal Conicyt CMM AFD170001 project. J.-R. C. and P. C. also acknowledge the hospitality of the Instituto de Física de San Luis Potosí. |
| S. M. has been supported by the Chair "Modelisation Mathematique et Biodiversite" of Veolia Environnement-Ecole Polytechnique-Museum national d'Histoire naturelle-Fondation X. P. C. and S. M. warmly thank the Basal Conicyt CMM AFD170001 project. J.-R. C. and P. C. also acknowledge the hospitality of the Instituto de Fisica de San Luis Potosi. |