After successful completion of the course, students are able to: work with probabilistic models arising from natural and economic sciences, to apply the tools from the theory of concentration of measure and large deviations in order to study their behavior on large scales (when the number of degrees of freedom or dimension of the problem tends to infinity),  to analyse the long-time behavior of stochastic processe, to estimate the speed of convergence of equilibrium of Markov chains, and to devise Monte Carlo Markov chain algorithms for concrete simulation problems

Advanced topics in the theory of probability, theory of stochasic processes and stochastic analysis: asymptotic behavior of stochastic processes (e.g. invariance principles, convergence to equilibrium for Markov chain and Monte Carlo sampling algorithms), probabilistic models in physics and in high-dimensional statistics and their large scale behavior (e.g.  phase transitions, symmetry breaking phenomena, concentration of measure and large deviation principles)

Lectures will take place in English. They will take place in person (with no streaming or recording); only in case of new lockdown they will be online.

I will use parts of the following book

- A. Kyprianou, Introductory lectures on fluctuations of Levy processes with applications

 Office hours for students: Wednesdays 2 p.m. - 3 p.m.

oral exam

Measure & Probability Theory 1 and 2.