Correlation Inequalities for Interacting Particle Systems with Duality

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other —a process which we call here the symmetric inclusion process (SIP)—or repel each other —a generalized version of the well-known symmetric exc...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical physics 2010-10, Vol.141 (2), p.242-263
Main Authors: Giardinà, C., Redig, F., Vafayi, K.
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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 prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other —a process which we call here the symmetric inclusion process (SIP)—or repel each other —a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction,—the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-010-0055-0