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Gibbs–non-Gibbs properties for evolving Ising models on trees

Aernout C. D. van Enter, Victor N. Ermolaev, Giulio Iacobelli, Christof Külske (2012)

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

In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each...

Homogenization results for a linear dynamics in random Glauber type environment

Cédric Bernardin (2012)

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

We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green–Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.

Hydrodynamic limit for a particle system with degenerate rates

P. Gonçalves, C. Landim, C. Toninelli (2009)

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

We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of kinetically constrained lattice gases (KCLG) which have been introduced and intensively studied in physical literature as simple models for the liquid/glass transition. Due to the degeneracy of rates there exist blocked configurations which do not evolve under the dynamics and in general...

Hydrodynamic limit of a d-dimensional exclusion process with conductances

Fábio Júlio Valentim (2012)

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

Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m  aj  αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on 𝕋 d , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d  ∂xk  ∂Wk  Φ(ρ). We also derive some properties of the operator ∑k=1d  ...

Hydrodynamical behavior of symmetric exclusion with slow bonds

Tertuliano Franco, Patrícia Gonçalves, Adriana Neumann (2013)

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

We consider the exclusion process in the one-dimensional discrete torus with N points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance N - β , with β ∈ [ 0 , ∞ ) . We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter β . If β ∈ [ 0 , 1 ) , the hydrodynamic limit is given by the usual heat equation. If β = 1 , it is given by a parabolic equation involving an operator d d x d d W , where W ...

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