Mark Kac Seminar
May 8, 2009
Location:
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11:15-13:00 |
speaker: Silke Rolles (München) |
title: Bayesian analysis for reversible Markov chains |
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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. |
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4:15-16:00 |
speaker: Franz Merkl (München) |
title: What
are crystals? (3) |
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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. |
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Mark Kac Seminar 2008-2009 |
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last updated: 18 dec 2008by Markus |