Ulysse Godreau: Exact results for the open asymmetric exclusion process and open questions

In this talk, we will consider the totally asymmetric simple exclusion process (TASEP) -- an exactly solvable paradigmatic model of non-equilibrium statistical mechanics -- with open boundary conditions. After introducing some general results on the phenomenology of the process and the formalism used to compute analytically the fluctuations of the particle currents, we will consider the Algebraic Bethe Ansatz solution of the process and show that the probability distribution of the time-integrated current has a nice expression in terms of a functions defined on a Riemann surface.