Geodesic
Interacting particle systems
Emmanuel Jacob1 ; Éric Luçon2 ; Laurent Ménard3 ; Cristina Toninelli4 ; Xiaolin Zeng5
1 Unité de Mathématiques Pures et Appliquées, ENS de Lyon site Monod, UMPA UMR 5669 CNRS, 46, allée d’Italie, 69364 Lyon Cedex 7, France
2 Université Paris Descartes, Sorbonne Paris Cité, Laboratoire MAP5, UMR 8145, 75270 Paris, France
3 Laboratoire Modal’X, Université Paris Nanterre, 200 avenue de la République, 92000 Nanterre, France
4 Laboratoire de Probabilités et Modèles Alèatoires CNRS-UMR 7599 Universités Paris VI-VII 4, Place Jussieu F-75252 Paris Cedex 05 France
5 Post-doc fellow at the School of Mathematical Sciences of Tel Aviv University
ESAIM. Proceedings, Tome 60 (2017), pp. 246-265.

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We present in this paper a number of recent and various works of statistical physics, which involve an interacting particle system. In kinetically constrained models, the particles are placed on ℤd, with local constraints on the dynamics, that can slow down the evolution and reproduce the behaviour of glassy systems. The contact process (or Suspected-Infected-Susceptible) is a simple model for the spread of an infection on a (general) graph. In the Kuramoto model, the motion of the particles is determined by a diffusion system with mean-field interaction. Finally, in the modeling of the vertex reinforced jump process (a particle that interacts with itself via its path), we show an unexpected link with an interacting particle system.
DOI : 10.1051/proc/201760246

Emmanuel Jacob 1 ; Éric Luçon 2 ; Laurent Ménard 3 ; Cristina Toninelli 4 ; Xiaolin Zeng 5

1 Unité de Mathématiques Pures et Appliquées, ENS de Lyon site Monod, UMPA UMR 5669 CNRS, 46, allée d’Italie, 69364 Lyon Cedex 7, France
2 Université Paris Descartes, Sorbonne Paris Cité, Laboratoire MAP5, UMR 8145, 75270 Paris, France
3 Laboratoire Modal’X, Université Paris Nanterre, 200 avenue de la République, 92000 Nanterre, France
4 Laboratoire de Probabilités et Modèles Alèatoires CNRS-UMR 7599 Universités Paris VI-VII 4, Place Jussieu F-75252 Paris Cedex 05 France
5 Post-doc fellow at the School of Mathematical Sciences of Tel Aviv University 
@article{EP_2017_60_a13,
     author = {Emmanuel Jacob and \'Eric Lu\c{c}on and Laurent M\'enard and Cristina Toninelli and Xiaolin Zeng},
     title = {Interacting particle systems},
     journal = {ESAIM. Proceedings},
     pages = {246--265},
     publisher = {mathdoc},
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     year = {2017},
     doi = {10.1051/proc/201760246},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201760246/}
}
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Emmanuel Jacob; Éric Luçon; Laurent Ménard; Cristina Toninelli; Xiaolin Zeng. Interacting particle systems. ESAIM. Proceedings, Tome 60 (2017), pp. 246-265. doi : 10.1051/proc/201760246. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760246/

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