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Hydrodynamical behavior of symmetric exclusion with slow bonds

Tertuliano FrancoPatrícia GonçalvesAdriana 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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