Math.Koll. am 11.10.06/Dr. R. Zweimueller

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG
zu einem
VORTRAG
im Rahmen der Habilitation
von
Dr. Roland Zweimueller
(Institut für Mathematik, Universitaet Wien)
mit dem Thema:

"Probability theory for infinite measure preserving transformations"

Abstract:
Mathematical models of systems evolving in time often come as deterministic
dynamical systems (reflecting detailled knowledge of the system, but
sometimes useless for long-term prediction), or as stochastic descriptions
(which allow an analysis of their asymptotic behaviour, but abandon much of
the available information). Ergodic theory and an emergent specialized
branch of probability theory attempt to bridge the gap between these two
worlds by rigorously studying "stochastic properties of deterministic
dynamical systems". By this we mean the investigation of the random
processes obtained if we regard measures on (rather than points in) the
phase space as proper descriptions of the actually available information
about the initial condition of the system. Typically, these processes do not
share the clear-cut dependence structure which defines (and enables an
analysis of) classical families of stochastic processes. Still, it is
possible to carry out the program of extending classical probabilistic
results to this framework for prototypical dynamical systems.

The purpose of this talk is to present some recent probabilistic results for
infinite measure preserving transformations, generalizing, for example,
classical results about random walks. The analytic core is a new method
enabling us to use ideas from renewal theory in this more general abstract
setup. It results in a new type of (surprisingly "soft") conditions which
admit easy verification in various classes of examples.

Zeit: Mittwoch, 11. Oktober 2006, 16.15 Uhr

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09

Harald Rindler
Klaus Schmidt