Sommaire:

Non-equilibrium systems have been studied extensively in the last 20 years. Unlike equilibrium, these systems are characterized by a breaking of reversibility at the microscopic level leading to the presence of currents at the macroscopic level. In one dimension, exact results have been obtained for the fluctuations of macroscopic quantities in several such systems, using tools including Bethe ansatz, the replica method, and random matrices. Two prominent examples are a discrete microscopic model of classical hard core particles hopping with a preferred direction (asymmetric simple exclusion process) and a continuous equation describing the stochastic evolution of a growing surface at large scales (Kardar-Parisi-Zhang equation).

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