I discuss the behavior of Loewner evolutions driven by a Levy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers.
This talk is based on joint work with Anne Schreuder (Cambridge).
The seminar will be held via zoom. Members of the department will receive the link and password via mail. Others interested are welcome to attend and can get the link by contacting one of the organisers (please inform us who you are).
19 October, 2021, 13:15
19 October, 2021, 14:15