6th Probability Day Erlangen-München

The probability day takes place on
Friday, January 26, 2007
at the mathematical institute of the Ludwig-Maximilian-Universität München in Room C 113.
Information how to get to the mathematical institute can be found here. It takes approximately 25 minutes to walk from the train station to the mathematical institute.

Programme

14:30 - 15:30 Federico Camia (Vrije Universiteit Amsterdam)
Conformal Loop Ensembles and Critical Percolation.
Abstract: Conformal Loop Ensembles (CLEs) are random collections of countably many loops in a planar domain characterized by certain conformal invariance and Markovian properties. They are conjectured to appear as scaling limits of various two- dimensional lattice models from statistical physics, including Ising, Potts and O(n) models. The scaling limit of two-dimensional critical percolation also gives rise to a CLE. This can be proved using the convergence of the percolation exploration path to the Stochastic (Schramm-)Loewner Evolution with parameter 6.
(Based on joint work with C.M. Newman.)
15:30 - 16:00 Coffee and tea
16:00 - 17:00 Markus Heydenreich (Technische Universiteit Eindhoven)
Critical percolation clusters on high-dimensional boxes.
Abstract: We consider "critical" bond percolation on a high-dimensional (finite) box, and discuss the size of the largest connected component under bulk and periodic boundary conditions. Interestingly, the periodic case shows the same asymptotic behaviour like the random graph model, that is obtained by percolation on a complete graph. This is in contrast to the case with bulk boundary conditions, where maximal critical clusters are asymptotically much smaller. Hence boundary conditions play an essential role.
(Based on joint work with Remco van der Hofstad.)
17:00 - 18:00 Anita Winter (Technion Haifa)
Coalescent processes arising in a study of diffusive clustering.
Abstract: We consider spatial coalescents on $\Z^2$., i.e, the partition elements have locations in $\Z^2$ and undergo migration and local coalescence. The coalescent will start with countably many partition elements in each side of a box of side-length $t^{\frac{\alpha}{2}}$ and is observed at time $t^\beta$ where $1\ge \beta\ge \alpha\ge 0$. We study both asymptotics as $t\to\infty$: for a fixed value of alpha as a process in beta and for a fixed beta as a process in alpha.
In the limit the so-called Kingman-type coalescent with rebirth arises.
(Joint work with Andreas Greven and Vlada Limic)

After the talks, there will be a dinner at the restaurant Cohen's, Theresienstrasse 31.
If you are not a speaker and need a hotel, we kindly ask you to book a hotel yourself. Speakers will be accomodated in Hotel Stefanie, which is located in five minutes walking distance from the mathematical institute.
Organizers: Hans-Otto Georgii (München), Andreas Greven (Erlangen), Gerhard Keller (Erlangen), Franz Merkl (München), and Silke Rolles (München).

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