Kinetically constrained lattice gases: Tagged particle diffusion

Kinetically constrained lattice gases (KCLG) are interacting particle systems on the integer lattice Z d with hard core exclusion and Kawasaki type dynamics. Their peculiarity is that jumps are allowed only if the configuration satisfies a constraint which asks for enough empty sites in a certain lo...

Full description

Saved in:
Bibliographic Details
Published inAnnales de l'I.H.P. Probabilités et statistiques Vol. 54; no. 4
Main Authors Blondel, O., Toninelli, C.
Format Journal Article
LanguageEnglish
Published Institut Henri Poincaré (IHP) 01.11.2018
Subjects
Mathematics
Probability
tagged particle
kinetically constrained models
Kawasaki dynamics
Online AccessGet full text

Cover

More Information
Summary:Kinetically constrained lattice gases (KCLG) are interacting particle systems on the integer lattice Z d with hard core exclusion and Kawasaki type dynamics. Their peculiarity is that jumps are allowed only if the configuration satisfies a constraint which asks for enough empty sites in a certain local neighborhood. KCLG have been introduced and extensively studied in physics literature as models of glassy dynamics. We focus on the most studied class of KCLG, the Kob Andersen (KA) models. We analyze the behavior of a tracer (i.e. a tagged particle) at equilibrium. We prove that for all dimensions d ≥ 2 and for any equilibrium particle density, under diffusive rescaling the motion of the tracer converges to a d-dimensional Brownian motion with non-degenerate diffusion matrix. Therefore we disprove the occurrence of a diffusive/non diffusive transition which had been conjectured in physics literature. Our technique is flexible enough and can be extended to analyse the tracer behavior for other choices of constraints. MSC 2010 subject classifications:60K35 60J27
ISSN:0246-0203
1778-7017
DOI:10.1214/17-AIHP873