Mark Kac Seminar

June 5, 2009






Location: Utrecht, KNG80, room 130


speaker: Dimitris Cheliotis (EURANDOM)

title: The critical curve for pinning of random polymers. A large deviations approach.


We consider a directed random polymer interacting with an interface that carries random charges some of which attract while others repel
the polymer. Such a polymer can be in a localized or delocalized phase, i.e., it stays near the interface or wanders away respectively.  The phase it chooses depends on the temperature and the average bias of the disorder. At a given temperature, there is a critical bias separating the two phases. A question of particular interest, and which has been studied extensively in the Physics and Mathematics literature, is whether the quenched critical bias differs from the annealed critical bias. When it does, we say that the disorder is relevant.

Using a large deviations result proved recently by Birkner, Greven, and den Hollander, we derive a variational formula for the quenched critical bias. This leads to a necessary and sufficient condition for disorder relevance that implies easily some known results as well as new one


speaker: Jeremy Clark (KU Leuven)

title: Central limit theorem for an inhomogeneous linear Boltzmann equation at infinite temperature.


I will discuss a class of linear Boltzmann equations describing a classical particle in a spatially inhomogeneous noisy environment.  The dynamics includes a periodic potential field and a noise whose statistics depend periodically on the location of the particle.  The model is set at infinite temperature and thus does not have energy relaxation.  In the long time limit, a central limit theorem emerges for the joint distribution in momentum and position in which the limiting form depends only on a spatial average of the noise.  I will finish by defining and discussing the quantum analog for the problem.   The quantum version has appeared in the physics literature on atoms in an optical lattice.


Mark Kac Seminar 2008-2009


last updated: 26 May 2009 by Markus