Condensation of SIP Particles and Sticky Brownian Motion

We study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing in...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical physics 2021-06, Vol.183 (3), Article 40
Main Authors: Ayala, Mario, Carinci, Gioia, Redig, Frank
Format: Article
Language:English
Subjects:
Brownian motion
Condensates
Convergence
Dirichlet problem
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Specific gravity
Statistical Physics and Dynamical Systems
Theoretical
Variance
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t . This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-021-02775-5