Mark Kac Seminar

May 8, 2009






Location: Utrecht, KNG80, room 130


speaker: Silke Rolles (München)

title: Bayesian analysis for reversible Markov chains


We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Polya's urn.

(Joint work with Persi Diaconis.)



speaker: Franz Merkl (München)

title:  What are crystals? (3)

This is the third and final lecture from a series of three lectures, starting March 6.


abstract (for the series): 


As is well-known from everyday knowledge, interacting molecules at thermal equilibrium at low temperature form cristals. At higher temperature, they undergo a melting transition to a liquid phase. From the viewpoint of statistical mechanics, these well-known facts are by far not understood.


The talks are concerned with the notion of spontaneous symmetry breaking in interacting particle systems. On the one hand, I will present a (over-)simplified model for a two-dimensional continuum particle system that spontaneously breaks rotational symmetry. On the other hand, by the famous Mermin-Wagner phenomenon, two-dimensional particle systems frequently show preservation of continuous symmetry. For example, Richthammer has recently shown that translational symmetry is preserved in two-dimensional hard-core particle systems.


The Mermin-Wagner phenomenon plays also a role in the recent understanding of linearly edge-reinforced random walks. There, absence of spontaneous breaking of a certain scaling symmetry plays an essential role.


(Joint work with Silke Rolles.)



Mark Kac Seminar 2008-2009


last updated: 18 dec 2008by Markus