Grosskinsky, Stefan, Redig, Frank and Vafayi, Kiamars (2013) Dynamics of condensation in the symmetric inclusion process. Electronic Journal of Probability, Volume 18 . Article number 66. doi:10.1214/EJP.v18-2720 ISSN 1083-6489.

Preview

Text WRAP_Grossinky_2720-14079-1-PB.pdf - Published Version Available under License Creative Commons Attribution. Download (562Kb) | Preview

Request Changes to record.

Abstract

The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the zero-range process, due to attractive interaction between the particles, the inclusion process can exhibit
a condensation transition. In this paper we present first rigorous results on the dynamics of the condensate formation for this class of models. We study the symmetric
inclusion process on a finite set S with total number of particles N in the regime of strong interaction, i.e. with independent diffusion rate m = mN → 0. For the case NmN → ∞ we show that on the time scale 1=mN condensates emerge from general homogeneous initial conditions, and we precisely characterize their limiting dynamics. In the simplest case of two sites or a fully connected underlying random walk kernel, there is a single condensate hopping over S as a continuous-time random walk. In the non fully connected case several condensates can coexist and exchange mass via intermediate sites in an interesting coarsening process, which consists of a mixture of a diffusive motion and a jump process, until a single condensate is formed. Our result is based on a general two-scale form of the generator, with a fast-scale neutral Wright-Fisher diffusion and a slow-scale deterministic motion. The motion of the condensates is described in terms of the generator of the deterministic motion and
the harmonic projection corresponding to the absorbing states of the Wright-Fisher diffusion.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Mathematical physics, Particles (Nuclear physics), Diffusion, Diffusion -- Mathematical models, Condensation, Condensation -- Mathematical models
Journal or Publication Title:	Electronic Journal of Probability
Publisher:	University of Washington. Dept. of Mathematics
ISSN:	1083-6489
Official Date:	2013
Dates:	Date Event 2013 Published
Volume:	Volume 18
Page Range:	Article number 66
DOI:	10.1214/EJP.v18-2720
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	24 December 2015
Date of first compliant Open Access:	24 December 2015
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/I014799/1

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads