Séminaire de Probabilités commun ICJ/UMPA

Two duality relations for Markov processes with an open boundary

by Chiara Franceschini (Modena (Italie))

Bâtiment Braconier, salle Fokko du Cloux (Université Lyon 1)

Bâtiment Braconier, salle Fokko du Cloux

Université Lyon 1


In this talk I will show how the same algebraic approach, which relies on the su(1,1) Lie algebra, can be used to construct two duality results. One is well-known: the two processes involved are the symmetric inclusion process and a Markov diffusion called Brownian Energy process. The other one is a new result in collaboration with C. Giardinà and R. Frasssek which involves a particle system of zero-range type, called harmonic process, and a redistribution model similar to the Kipnis-Marchioro-Presutti model. For these models all moments in the stationary nonequilibrium state can be explicitly computed and we can characterize the invariant measure as a mixture of inhomogeneous products of exponential distributions.