Journal of Statistical Physics

, Volume 141, Issue 2, pp 242–263 | Cite as

Correlation Inequalities for Interacting Particle Systems with Duality

  • C. Giardinà
  • F. Redig
  • K. Vafayi


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.


Exclusion process Duality Correlation inequalities Heat conduction 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Modena and Reggio Emilia UniversityReggio EmiliaItaly
  2. 2.IMAPPUniversiteit NijmegenNijmegenThe Netherlands
  3. 3.Mathematisch Instituut Universiteit LeidenLeidenThe Netherlands

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