The inclusion process: duality and correlation inequalities

C. Giardina; F. Redig; K. Vafayi

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arXiv · 0906.4664

The inclusion process: duality and correlation inequalities

C. Giardina·F. Redig·K. Vafayi

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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.

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BibTeX RIS

C. Giardina, F. Redig, K. Vafayi. 2009-06-25. The inclusion process: duality and correlation inequalities. https://arxiv.org/abs/0906.4664

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