KINETICALLY CONSTRAINED PARTICLE SYSTEMS ON A LATTICE

Oriane Blondel 1
1 Modélisation stochastique
LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : This thesis is about stochastic lattice models of particle systems with Glauber dynamics and kinetic constraints (KCSM), more specifically the East and FA-1f models. These models were introduced in physics for the study of glassy systems. In this document one finds first a summary of its contents (in French), then three introductory chapters in which I present the context of my works and show both what what my contributions add to the picture and on which notions and techniques they rely. In my presentation of KCSM, I focus on objects and results that are directly related to my research. Finally my papers are assembled in the Appendix, in some cases with extensions that were cut off for publication. The first chapter is an introduction to KCSM. The second chapter presents non-equilibrium issues for KCSM. First I give results about out-of-equilibrium local relaxation; in the FA-1f model it is a joint work with N. Cancrini, F. Martinelli, C. Roberto and C. Toninelli. Then I study the progression of a front in the East model and show a shape theorem as well as an ergodicity result for the process seen from the front. This result relies on quantifying the local relaxation of the process seen from the front rather than using classic sub-additivity arguments. The last chapter explores low-temperature (or high density) dynamics of KCSM. I first recall asymptotic results about East and FA-1f spectral gaps and offer some heuristics and conjectures. I then focus on the low temperature behaviour of the diffusion coefficient of a tracer in a KCSM, so as to give rigorous answers to questions raised in the physics literature.
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https://tel.archives-ouvertes.fr/tel-00913896
Contributor : Oriane Blondel <>
Submitted on : Wednesday, December 4, 2013 - 3:02:46 PM
Last modification on : Sunday, March 31, 2019 - 1:38:02 AM
Long-term archiving on : Saturday, April 8, 2017 - 3:50:57 AM

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  • HAL Id : tel-00913896, version 1

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Oriane Blondel. KINETICALLY CONSTRAINED PARTICLE SYSTEMS ON A LATTICE. Probability [math.PR]. Université Paris-Diderot - Paris VII, 2013. English. ⟨tel-00913896⟩

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