Mathematisches Kolloquium

Zusammenfassung: I will present a survey of recent results about the long time asymptotic behaviour of random processes with long memory due to some rather natural local self-intaraction (self-repellence) of the trajectories. Typical examples are the so-called myopic (or "true") self-avoiding random walk and the self-repelling Brownian polymer models. (These appeared independently in the physics, respectively, probabilistic literature in the 1980-ies.) The long time asymptotics of the displacement is expected to be robust (not depending on some microscopic details), but dimension dependent. It is expected that in 1d the motion is strongly superdiffusive, with time-to-the-two-thirds scaling; in 2d the motion is marginally superdiffusive with logarithmic multiplicative correction in the scaling; in three and more dimensions the displacement is diffusive. For some particular models some of these conjectures have been recently proved. The talk will be based on joint work with I. Horvath (Budapet), P. Tarres (Oxford), B. Valko (Madison WI), B. Veto (Budapest).

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.