A coupling construction for spin systems with infinite range interactions

François Ezanno (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has already been widely used (\cite{Gray}, \cite{GrayGriffeath}, \cite{HolleyStroock}, \cite{Liggettarticle}) but our construction brings a new insight to understand why it is natural. \\The process is first constructed as a limit of finite spin systems. Then we identify its generator and give a simple criterion for a measure to be invariant with respect to it.

Mots clés: Interacting particle systems; graphical construction; coupling

Domaines: Probabilités [math.PR]

François Ezanno. A coupling construction for spin systems with infinite range interactions. Markov Processes And Related Fields, 2013, 18 (2), pp.201--214. ⟨hal-00817281⟩