12th Meeting of AiOs in Stochastics

The twelfth meeting of the AiOs (PhD students) in Stochastics in the Netherlands will take place from 10 - 12  May 2004. This meeting is organized by the AiO Network Stochastics and is supported by the research schools MRI and Stieltjes Institute. The meetings continue the tradition of AiO meetings following the Bijeenkomst Stochastici in Lunteren, at a different location, a different time,  and in a different format.

The meeting consists of two short courses, one in probability and one in statistics, and lectures by the participants. The purpose is both to learn topics of current research interest and to become acquainted with the work of other aios in the Netherlands.

The meeting is sponsored by the research schools Stieltjes Institute and Mathematical Research Institute (MRI).
 

Programme
The short courses are given by Remco van der Hofstad and Pascal Massart. See below for titles and abstracts.
The meeting will start on Monday at 10.30 and will end on Wednesday after lunch. For a detailed programme see below.

Location
The meeting will be held in  building "Stalheim" (see picture)  of
 Conferentie Centrum De Hoorneboeg
 Hoorneboeg 5
 1213 RE Hilversum
  035 - 577 1231

Registration
Registration is possible electronically through the registration form.

Conference Fee
The total fee for the conference and two nights overnight stay in building Stalheim and meals from Monday lunch to Wednesday lunch is 50 euros for AiOs affiliated with MRI or Stieltjes Institute. The total fee is 165 euros for all others. See the registration form for specifics on payment.

Further Information
For further information contact the organizers Ronald Meester and Aad van der Vaart, or Maryke Titawano for practical matters.
 
 
 

Detailed Program
 

Abstracts and Titles

Remco van der Hofstad
Self-avoiding walks and percolation above the upper critical dimension.

Abstract
Self-avoiding walk and percolation are caricature models for linear polymers and porous media. Many other statistical mechanical models are expected to show similar behaviour as these two basic models, such as the existence of phase transitions and critical exponents, which turns these models into key examples in the field. It remains a major challenge to prove the scaling behaviour in these models at criticality.
Self-avoiding walk and percolation models have an `upper critical dimension', above which the behaviour ceases to depend on the dimension, and the phase transition becomes close to the phase transition for simpler models such as random walks and branching random walk. In contrast to the original models, these simpler or `mean-field' models do not self-interact, which makes their investigation feasible. In these lectures, we will investigate critical self-avoiding walk and percolation models, as well as their close friends the contact process and lattice trees, above the upper critical dimension.
The main tool is the `lace expansion', which perturbs the interacting model around the mean-field model. The expansion can be derived using sophisticated inclusion-exclusion arguments. We will derive the lace expansion for self-avoiding walk and oriented percolation, and show how the lace expansion can be used to prove the existence of several critical exponents. We will also describe the recently discovered relations between percolation models above the upper critical dimension and `measure valued diffusions' such as super-Brownian motion.
We will assume no previous knowledge of the models nor of the lace expansion, and the necessary background will be provided during the course.

Pascal Massart
Model selection and concentration inequalities.

Abstract
Model selection is a classical topic in statistics. The idea of selecting a model via penalizing a log-likelihood type criterion goes back to the early seventies with the pioneering works of Mallows and Akaike. One can find many consistency results in the literature for such criteria. These results are asymptotic in the sense that one deals with a given number of models and the number of observations tends to infinity. One of the two main goals of the course will be to provide an overview of a non asymtotic theory for model selection which has emerged during these last ten years. In various contexts of function estimation it is possible to design penalized log-likelihood type criteria with penalty terms depending not only on the number of parameters defining each model (as for the classical criteria) but also on the "complexity" of the whole collection of models to be considered. The performance of such a criterion can be analyzed via non asymptotic risk bounds for the corresponding penalized estimator which express that it performs almost as well as if the "best model" (i.e. with minimal risk) were known. For the relevance of these methods, it is desirable to get a precise expression of the penalty terms involved in the penalized criteria on which they are based. This is one reason why this approach heavily relies on concentration inequalities, the prototype being Talagrand's inequality for empirical processes. The course will also be devoted to concentration inequalities per se. More precisely we shall develop the entropy method initiated by Michel Ledoux which leads to concentration inequalities in a very simple and efficient way.