Continuous and Discrete Random Spatial Processes

20 - 29 April 2004

Venue: Lorentz Center@Oort

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Spatial stochastic processes play an important role in physics and mathematics. The role of space gains additional interest when the usual spatial symmetries are extended to include invariance for scaling. This typically leads one to consider the scaling limit.  In theoretical physics, a natural description of this limit is by means of field theory. However, this description has remained unsatisfactory to mathematicians as the results have withstood formalisation into rigorous proofs. Only very recently some of the classical results of universal critical behavior in two dimensional systems have found rigorous confirmation and extension. A new method, now known as Stochastic Loewner Evolution (SLE), has been the key to this development. It is open to mathematical proof and it has led to a great number of very strong results.  It has sparked a great amount of interdisciplinary communication between physicists and mathematicions.

There are several other developments in spatial stochastic processes that also call for renewed interchange between physics and mathematics. Random walks on random structures has recently seen important progress, and rigorous multiscale methods have been developed to handle a variety of problems.  There has also been considerable progress in the mathematical description of self-organized criticality.

From the physics community there have been many observations on boundary and bulk correlations of percolation and on connections of this problem with quantum spin chains, super symmetric fermion models and stochastic models. These observations can be formulated in precise mathematical conjectures. Some of these conjectures give a connection with long standing combinatorial problems.

The workshop gives special attention to (but is certainly not estricted to) these and related developments. The main goal is to bring together people from different backgrounds who work on Random Spatial Processes. We hope it will lead to new collaborations, ideas and results.

Preliminary list of speakers (the total number of speakers is planned to be 19):

Martin Barlow – UBC Michel Bauer – Saclay Denis Bernard – Saclay Federico Camia – EURANDOM John Cardy – Oxford Bertrand Duplantier – Saclay Jan de Gier - Melbourne Remco van der Hofstad – TUE Harry Kesten – Cornell Ronald Meester – VU Charles Newman – Courant Steffen Rohde - Seattle Senya Shlosman - Marseille Vladas Sidoravicius – IMPA Yuri Stroganov – IHEP Protvino Balint Toth - Budapest Wendelin Werner – Orsay Paul Wiegman – Chicago

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