| Issue |
ESAIM: ProcS
Volume 68, 2020
Journées MAS 2018 - Sampling and Processes
|
|
|---|---|---|
| Page(s) | 52 - 72 | |
| DOI | https://doi.org/10.1051/proc/202068004 | |
| Published online | 10 June 2020 | |
Dynamics of interacting particle systems*,**,***
1 Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR5208, Institut Camille Jordan, F-69622 Villeurbanne, France,
e-mail: blondel8math.univ-lyonl.fr
2 Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), UPEM, UPEC, CNRS, F-94010, Créteil, France
3 Learning, Data & Robotics Lab - ESIEA, Paris, France
e-mail: deshayes8esiea.fr
4 Université Paris-Dauphine, PSL Research University, Ceremade, CNRS, 75775 Paris Cedex 16, France
e-mail: labbe@ceremade.dauphine.fr
5 LPSM UMR 8001, Université Paris Diderot, Sorbonne Paris Cité, CNRS, 75013 Paris, France
e-mail: marecheSlpsm.paris.
6 Inria, Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
e-mail: marielle.simon8inria.fr
We collect here recent results covering various aspects of the dynamical properties of interacting particle systems. In Section 1 we study the hydrodynamic limit of a facilitated exclusion process. Section 2 evidences a cutoff phenomenon for the mixing time of the weakly asymmetric exclusion process. Section 3 presents a study of the infection time in the Duarte model. Finally, Section 4 presents the study of a front propagation in the FA-If model.
Résumé
Nous rassemblons ici des résultats récents sur différentes propriétés dynamiques des systèmes de particules en interaction. En section 1 on étudie la limite hydrodynamique d’un processus d’exclusion facilité. La section 2 met en évidence un phénomène de cutoff pour le temps de mélange du processus d’exclusion faiblement asymétrique. La section 3 présente une étude du temps d’infection du modèle de Duarte. Enfin, la section 4 présente l’étude de la propagation d’un front dans le modèle FA-lf.
O.B. acknowledges support from the ANR projects LSD (ANR-15-CEj0-0020) and MALIN (ANR-16-CE93-0003).
M.S. acknowledges support from the Labex CEMPI (ANR-ll-LABX-0007-01), from the project EDNHS (ANR-lj-CEZS- 0011) of the French National Research Agency (ANR) and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement n° 71573)).
© EDP Sciences, SMAI 2020
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