Lipschitz Lectures

Anomalous dynamics and disordered systems

Gérard Ben Arous (Courant Institute of Mathematical Sciences, New York University)


Date, Time, and Location:

Monday, November 20, 2017,
4 - 6 p.m., Großer Hörsaal, Wegelerstr. 10, 53115 Bonn

Friday, November 24, 2017,
2 - 4 p.m., Kleiner Hörsaal, Wegelerstr. 10, 53115 Bonn

 

Monday, January 8, 2018
2 - 4 p.m., Lipschitz lecture hall, Endenicher Allee 60, 53115 Bonn

Thursday, January 11, 2018
2 - 4 p.m., Lipschitz lecture hall, Endenicher Allee 60, 53115 Bonn

 

Abstract

The central limit theorem, and its avatars, is the best example of a broad universality class. For a very wide class of systems, random or not, dynamics are governed by Brownian motion, or normal diffusion. This is the core of homogenization theory and of a large part of probability theory.
We are interested here in mechanisms of anomalous diffusion, where this fails. We will mainly insists on mechanisms for anomalously slow dynamics, only mentioning in passing those for anomalously fast ones. These slow dynamics are usually induced by trapping regions, themselves created by strong disorder of the random landscapes in which the dynamics evolve.
We will give a broad picture of the known mechanisms in a few of the most important examples, in particular for diffusion in critical percolation clusters or, as de Gennes coined it in 1976, ‘the ant in the labyrinth”, and for a very different class of examples of very slow dynamics, i.e. relaxation and aging of  spin glasses. We will show how these different mechanisms can be related to an abstract model of trapping, which is relevant for essentially all known examples. We will also show what can be said today for short time scales in these very long time dynamics, and how this could be potentially useful for random exploration of the complex landscapes of machine learning.

 

In case you are interested in participating, please fill out the application form.