After successful completion of the course, students are able to show excellence in special fields of probability.
After having successfully completed the course, students are able to solve complex problems in the modeling and processing of tasks in the field of higher probability theory
The course will consiste of two independent parts.
The first part (teacher: F. Toninelli) will focus on statistical mechanics and in particular on the so-called two-dimensional dimer model. Detailed contents: Kasteleyn theory for dimer model on planar graphs, correlation functions, infinite volume Gibbs measures, limit shape phenomenon, convergence of fluctuations to the Gaussian Free Field.
The second part (teacher: K. Grill) will focus on special topics in stochastic processes, selected from: Wiener process, random walks, the invariance principle and laws of the iterated logarithm, Martingale, characteristic functions, stable distributions, interrelations of stochastic processes, risk and extreme value theory, ergodics
