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Non-equilibrium fluctuations for the slow boundary symmetric exclusion

Presented by: 
Patricia Gonçalves Instituto Superior Técnico, Lisboa
Date: 
Monday 22nd October 2018 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, I will present the symmetric simple exclusion process in contact with slow stochastic reservoirs which are regulated by a factor $n^{-\theta}$, $\theta\geq 0$. I will review the hydrodynamic limit and the goal of my talk is to present the non-equilibrium fluctuations for this model. Depending on the range of the parameter $\theta$ we obtain processes with various boundary conditions. As a consequence of the previous result together with an application of the matrix ansatz method - which gives us information on the stationary measure for the model - we deduce the non-equilibrium stationary fluctuations. The main ingredient to prove these results is the derivation of precise bounds on the two-point space-time correlation functions.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons