Non-equilibrium fluctuations for the slow boundary symmetric exclusion

SRQW02 - Quantum field theory, renormalisation and stochastic partial differential equations

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.

This talk is part of the Isaac Newton Institute Seminar Series series.