Courses in Probability Theory

During the Fall term 2007:

• Wahrscheinlichkeitstheorie by Alain-Sol Sznitman

• Special Topics in Probability by Jiri Cerny

Aging in dynamics of disordered systems

It was observed experimentally that certain real-world materials relax very slowly to equilibrium and, moreover, the relaxation manifests some unusual features like aging, rejuvenation and memory effects. The goal of the lecture is to present some recent mathematical results explaining some of these features in the context of Markovian dynamics in disordered systems, in particular in mean-field spin glasses. In order to achieve the goal, the lecture will include some more advanced chapters from the theory of extremes of i.i.d. random variables and of Gaussian processes, from the renewal theory and from the theory of Levy processes. Some results on random walks on graphs will also be introduced.

The lecture should be essentially self-contained. Only basic knowledge of Markov chains and theory of i.i.d. random variables will be required.