The inclusion process: duality and correlation inequalities
Abstract
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.
Cite
@article{arxiv.0906.4664,
title = {The inclusion process: duality and correlation inequalities},
author = {C. Giardina and F. Redig and K. Vafayi},
journal= {arXiv preprint arXiv:0906.4664},
year = {2010}
}
Comments
This is a new version: correlation inequalities for the Brownian energy process are added, and the part of the asymmetric inclusion process is removed.