LARGE DEVIATIONS FOR THE EXCLUSION PROCESS WITH A SLOW BOND

LARGE DEVIATIONS FOR THE EXCLUSION PROCESS WITH A SLOW BOND

We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N−1, where N is the scaling parameter. This model has been considered in pre...

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Veröffentlicht in:The Annals of applied probability 2017-12, Vol.27 (6), p.3547-3587
Hauptverfasser: Franco, Tertuliano, Neumann, Adriana
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Boundary conditions
Fluid mechanics
Hydrodynamic equations
Probability
Scaling
Variations
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description We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the slow bond, has associated transition rate of value N−1, where N is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynamical large deviations estimates in the diffusive scaling. The main challenge here is the fact that the presence of the slow bond gives rise to Robin's boundary conditions in the continuum, substantially complicating the large deviations scenario.
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subjects Boundary conditions
Fluid mechanics
Hydrodynamic equations
Probability
Scaling
Variations
title LARGE DEVIATIONS FOR THE EXCLUSION PROCESS WITH A SLOW BOND
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