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).
webmaster,