For­schungs­se­mi­na­re "Kom­ple­xe Quan­ten­sys­te­me" & "Wahr­schein­lich­keits­the­o­rie": Frank Aurzada (Darm­stadt) & Pas­cal Mit­ten­büh­ler (Pa­der­born)

Frank Aurzada (Darmstadt)
Breaking a chain of interacting Brownian particles
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise (quadratic) potential, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of
slow speed and small Brownian noise. We study the instant when the chain "breaks", that is, the distance between two neighboring particles becomes larger than a certain limit. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise. We prove weak limit theorems for the break time and the break position for each regime. On a separate page, we study the behaviour of the system when the number of particles tends to infinity. This is joint work with Volker Betz and Mikhail Lifshits

Pascal Mittenbühler (Paderborn)
Persistence probabilities of a smooth self-similar anomalous diffusion process
We first introduce the notion of persistence probabilities of stochastic processes and their asymptotic behaviour for large times. We then consider the persistence probability of a certain parameter dependent fractional Gaussian process that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. As this class of processes exhibits polynomially decaying persistence probabilities, we are interested in the polynomial order and study its behaviour close to the boundary of the parameter range.