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The time evolution of the probability distribution of a Markov process is given by a generator in a fashion that is formally very similar to the time evolution of the (complex) probability amplitude of a quantum system in imaginary time. This correspondence allows for the import of technical tools and notions from quantum mechanics to the study of stochastic processes (and vice versa) which has proved to be useful particularly in the context of stochastic interacting particles and quantum spin systems. This mini-course begins with an introduction into the formal aspects of this relationship. In the second part we discuss as applications: (a) Symmetry and duality, (b) Large deviations and Non-hermitian quantum mechanics, and, briefly, (c) Large-scale behaviour.

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Gunter Schütz, FZ Jülich
HS III
Contact: Joachim Krug