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Abstract: These notes are based on lectures delivered by the authors at a Langeoogseminar of SFB-TR12 -Symmetries and universality in mesoscopic systems- to amixed audience of mathematicians and theoretical physicists. After a briefoutline of the basic physical concepts of equilibrium and nonequilibriumstates, the one-dimensional simple exclusion process is introduced as aparadigmatic nonequilibrium interacting particle system. The stationary measureon the ring is derived and the idea of the hydrodynamic limit is sketched. Wethen introduce the phenomenological Kardar-Parisi-Zhang KPZ equation andexplain the associated universality conjecture for surface fluctuations ingrowth models. This is followed by a detailed exposition of a seminal paper ofJohansson that relates the current fluctuations of the totally asymmetricsimple exclusion process TASEP to the Tracy-Widom distribution of randommatrix theory. The implications of this result are discussed within theframework of the KPZ conjecture.



Author: Thomas Kriecherbauer, Joachim Krug

Source: https://arxiv.org/







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