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Events
Fall School on Statistical Mechanics and 5th Annual PhD Student Conference in Probability

MPI für Mathematik in den Naturwissenschaften Leipzig

G3 10 (Lecture hall)

conference

07/09/2009 12/09/2009

Fall School on Statistical Mechanics and 5th Annual PhD Student Conference in Probability

Three mini-courses: Sept. 7 (afternoon)- Sept. 9 (afternoon).

PhD Students’ conference: Sept. 10 (afternoon)- Sept. 12 (noon).

The fifth PhD students’ conference is jointly hosted by the IMPRS MIS Leipzig, the Research Academy Leipzig and the DMV Fachgruppe Stochastik. PhD students are expected to participate and/or present a 25- minute talk on an area within Probability.

Speakers

Christian Bartsch

Universität Münster

Marek Biskup

UCLA

Erwin Bolthausen

Universität Zürich

Gioia Carinci

Università degli Studi de L'Aquila

Sören Christensen

Universität Kiel

Alex Drewitz

TU Berlin

Andreas Janoschek

TU Darmstadt

Georg Menz

Universität Bonn

Guido Montufar

MPI MIS

Kai-Friederike Oelbermann

Universität Augsburg

Stiene Riemer

Universität Kiel

Felix Rubin

University of Zurich

Andre Schlichting

MPI MIS

Sylvia Schmidt

Universität Leipzig

Reik Schottstedt

TU Berlin

Roland Seydel

MPI MIS

Herbert Spohn

TU München

Philipp Thomann

Universität Zürich

Tat Dat Tran

MPI MIS

Jörg Vorbrink

Universität Bielefeld

Program

13:00 - 13:01	Fall School on Statistical Mechanics
14:00 - 15:30	Erwin Bolthausen (Universität Zürich, Zürich, Switzerland) Random Walk in Random Environment
15:30 - 16:00	Coffee break
16:00 - 17:30	Herbert Spohn (TU München, München, Germany) Stochastic Growth Processes In my minicourse I explain growth models in the Kardar-Parisi-Zhang universality class in one spatial dimension. In particular I cover various growth models, their stationary measures, scaling behavior, the link to tiling problems, directed last passage percolation, and to random matrices.
18:00 - 19:00	Wine and cheese party

09:00 - 10:30	Marek Biskup (UCLA, Los Angeles, USA) The Random Conductance Model In the random conductance model, each edge of the hypercubic lattice is assigned a positive and finite random variable called the conductance. The resulting (random) resistor network is directly linked to a Markov chain --- referred to, invariably, as a random walk among random conductances --- where at each step the walk chooses a neighbor at random with probability proportional to the conductance of the corresponding edge. The conductances are distributed according to a translation-invariant, or even iid, law; the properties of the random walk are studied against a typical sample from this law (these are the so called quenched problems). In my three lectures I will discuss the following facts/situations:(1) The proof of recurrence and transience for this random walk and the connection with effective resistivity.(2) The proof of an invariance principle for the path of the random walk in the case when the conductances are bounded away from zero and infinity (so called elliptic case).(3) Extensions to non-elliptic situations (random walk on the supercritical percolation cluster, regular and anomalous heat-kernel decay). I will finish with an outlook of problems awaiting solutions and possible directions of future research. My contributions to this field are based on joint works with N. Berger, T. Prescott, G. Kozma and C. Hoffman.
10:30 - 11:00	Coffee break
11:00 - 12:30	Erwin Bolthausen (Universität Zürich, Zürich, Switzerland) Random Walk in Random Environment
12:30 - 14:00	Lunch
14:00 - 15:30	Herbert Spohn (TU München, München, Germany) Stochastic Growth Processes
15:30 - 16:00	Coffee break
16:00 - 17:30	Marek Biskup (UCLA, Los Angeles, USA) The Random Conductance Model

09:00 - 10:30	Erwin Bolthausen (Universität Zürich, Zürich, Switzerland) Random Walk in Random Environment
10:30 - 11:00	Coffee break
11:00 - 12:30	Herbert Spohn (TU München, München, Germany) Stochastic Growth Processes
12:30 - 14:00	Marek Biskup (UCLA, Los Angeles, USA) The Random Conductance Model

13:00 - 13:01	5th Annual PhD Student Conference in Probability
13:45 - 14:45	Opening
14:00 - 14:25	Guido Montufar (MPI MIS, Leipzig, Germany) Information geometry of mean-field methods
14:30 - 14:55	Georg Menz (Universität Bonn, Bonn, Germany) A new covariance estimate for Gibbs measures
15:00 - 15:25	Andre Schlichting (MPI MIS, Leipzig, Germany) A stochastic Becker-Doering type interacting particle systems
15:30 - 16:00	Coffee break
16:00 - 16:25	Philipp Thomann (Universität Zürich, Zürich, Switzerland) On a Generalization of the Sherrington-Kirkpatrick model Many calculations on the SK-Model use its quite special properties. In order to understand the problem more thoroughly we treat a generalized version where spins are not constrained to Ising type. We calculate its free energy by use of the ideas appearing in Talagrand (2009).
16:30 - 16:55	Roland Seydel (MPI MIS, Leipzig, Germany) Impulse control of credit portfolios
17:00 - 17:25	Jörg Vorbrink (Universität Bielefeld, Bielefeld, Germany) Optimal stopping in finance in multiple prior model

09:00 - 09:25	Stiene Riemer (Universität Kiel, Kiel, Germany) On Random Matrices
09:30 - 09:55	Felix Rubin (University of Zurich, Zurich, Switzerland) Scaled limit for the largest eigenvalue from the generalized Cauchy random matrix ensemble In this talk, we are interested in the asymptotic properties for the largest eigenvalue of the Hermitian random matrix ensemble, called the Generalized Cauchy ensemble $GCy$, whose eigenvalues PDF is given by $$\textrm{const}\cdot\prod_{1\leq j-1/2$ and where $N$ is the size of the matrix ensemble. We will see that for this ensemble, the appropriately rescaled largest eigenvalue converges in law. We also express the limiting probability distribution in terms of some non-linear second order differential equation. Eventually, we show that the convergence of the probability distribution function of the re-scaled largest eigenvalue to the limiting one is at least of order $(1/N)$.
10:00 - 10:25	Christian Bartsch (Universität Münster, Münster, Germany), Michael Kochler, Thomas Kochler Survival of a Branching Random Walk in Random Environment We consider a particular Branching Random Walk in Random Environment (BRWRE) on $N_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which depends on the location) and move either one step to the right (with a probability in $(0,1]$ which may also depend on the location) or stay in the same place. We give criteria for local and global survival and show that global survival is equivalent to exponential growth of the moments.
10:30 - 11:00	Coffee break
11:00 - 11:25	Alex Drewitz (TU Berlin, Germany) Ballisticity Criteria for Random Walk in Random Environments Consider a random walk in a uniformly elliptic i.i.d. random environment in dimensions $d\ge 2$. In 2002, Sznitman introduced for each $\gamma\in (0,1)$ the ballisticity conditions $(T)_\gamma$ and $(T'),$ the latter being defined as the fulfilment of $(T)_\gamma$ for all $\gamma\in (0,1)$. He proved that $(T')$ implies ballisticity and that for each $\gamma\in (0.5,1)$, $(T)_\gamma$ is equivalent to $(T')$. It is conjectured that this equivalence holds for all $\gamma\in (0,1)$. Here we prove that for $\gamma\in (\gamma_d,1)$, where $\gamma_d$ is a dimension dependent constant taking values in the interval $(0.366,0.388)$, $(T)_\gamma$ is equivalent to $(T')$.
11:30 - 11:55	Sören Christensen (Universität Kiel, Kiel, Germany) On Optimal Stopping
12:00 - 12:25	Reik Schottstedt (TU Berlin, Berlin, Germany) Asymptotics of quantization problems
12:30 - 12:55	Kai-Friederike Oelbermann (Universität Augsburg, Augsburg, Germany) Apportionment methods in the European Parliament Election
15:00 - 16:00	Excursion - Canoeing

09:30 - 09:55	Sylvia Schmidt (Universität Leipzig, Leipzig, Germany) The Parabolic Anderson model with time dependent diffusion speed
10:00 - 10:25	Tat Dat Tran (MPI MIS, Leipzig, Germany) From Right-Fischer models to Kolmogorov equations and some geometrical interpretation
10:30 - 11:00	Coffee break
11:00 - 11:25	Gioia Carinci (Università degli Studi de L'Aquila, L'Aquila, Italy) Random Hysteresis Loops
11:30 - 11:55	Andreas Janoschek (TU Darmstadt, Germany) On particle filter

Participants

Christian Bartsch

Universität Münster

Marek Biskup

UCLA

Erwin Bolthausen

Universität Zürich

Gioia Carinci

Università degli Studi de L'Aquila

Sören Christensen

Universität Kiel

Alex Drewitz

TU Berlin

Andreas Janoschek

TU Darmstadt

Michael Kochler

Universität Münster

Thomas Kochler

Universität Münster

Noemi Kurt

TU Berlin

Georg Menz

Universität Bonn

Guido Montufar

MPI MIS

Kai-Friederike Oelbermann

Universität Augsburg

Stiene Riemer

Universität Kiel

Felix Rubin

University of Zurich

Johannes Rueß

Universität Tübingen

Andre Schlichting

MPI MIS

Sylvia Schmidt

Universität Leipzig

Felix Schneider

Universität Mainz

Reik Schottstedt

TU Berlin

Roland Seydel

MPI MIS

Herbert Spohn

TU München

Benedikt Tebbe

Universität Münster

Philipp Thomann

Universität Zürich

Tat Dat Tran

MPI MIS

Jörg Vorbrink

Universität Bielefeld

Scientific Organizers

Mathias Becker

Universität Leipzig

Wolfgang König

Universität Leipzig

Chiranjib Mukherjee

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Administrative Contact

Katja Bieling

Max Planck Institute for Mathematics in the Sciences Contact via Mail