Gunter Schütz

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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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FZ Jülich
HS III
Contact: Joachim Krug