Kolloquium der Bielefeld Graduate School in Theoretical Sciences
Vortragende: Sabine Jansen (LMU München)
Titel: Condensation, big jump and heavy tails: from phase transitions to probability
Abstract: Ice melts, water evaporates – these are everyday experiences of phase transitions. The explanation of this macroscopic phenomenon from microscopic laws belongs to the realm of statistical physics, which treats matter as a composite system made up of many individual „agents“ with random behavior. From a mathematician’s point of view, a fully rigorous understanding still eludes us. The search for it leads to questions in probability that open up surprising connections: toy models for surface tension of liquid droplets build on heavy-tailed variables used in insurance mathematics; a big jump made by a random walker is a condensation phenomenon in disguise. The talk explains some of these connections and presents open problems and partial answers.