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Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford, Li Wu (2008)

Open Mathematics

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than 7 + 41 2 and obeys some natural regularity conditions.

Couplings, attractiveness and hydrodynamics for conservative particle systems

Thierry Gobron, Ellen Saada (2010)

Annales de l'I.H.P. Probabilités et statistiques

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived markovian coupled process (ξt, ζt)t≥0 satisfies: (A) if ξ0≤ζ0 (coordinate-wise), then for all t≥0, ξt≤ζt a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on ℤd such that, in each transition, k particles may jump from a site x to another site y,...

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