Random spatial processes

Programme theme

Many physical processes may be modelled using random processes involvingspace and (possibly) time; for example, the spread of disease, the structure of disordered media, the growth of crystals. Two of the principal targets of the theory of such random spatial processes are to understand the nature of phase transitions, and to describe the geometry of evolving processes. There has emerged recently a body of powerful techniques, and progress is being made on some of the hardest problems. During this programme, probabilists and theoretical physicists will pursue such questions for interacting particle processes, percolation, random media, and models of population growth, as well as for continuum limits of such processes.

Participation

Long Stay Visitors

Tom Liggett, Chuck Newman, and Ed Perkins are acting as Scientific Advisors. Tom Mountford has been appointed to the Rosenbaum Fellowship.

The following are the prospective stays of long-term visitors who have accepted invitations:

P. Scalia-Tomba (Stockholm), DB. Abraham (Oxford), K. Alexander (USC), M. Barlow (UBC), J. van den Berg (Amsterdam) 1 Aug -- 30 Nov, A. DeMasi (L'Aquila), R. Dobrushin (Moscow) 1 Sep -- 30 Nov, P.Donnelly (QMW, London), P. Ferrari (Sao Paulo), A. Gandolfi (Berkeley) 1 Aug -- 15 Nov, G. Grimmett (Cambridge), H. Higuchi (Kobe), M. Keane (Delft), F. Kelly (Cambridge), H. Kesten (Cornell), T. Lawler (Duke), T. Liggett (UCLA), T. Mountford (UCLA), C. Newman (Courant), P. Pemantle (Madison), E. Presutti (Rome), R> Schonmann (UCLA) 1 Jul -- 15 Sep, S. Shlosman (Moscow/Irvine), G. Slade (McMaster)

Others who expect to visit for a substantial period include

B. Bolthausen (Zurich) 12 Sep -- 25 Sep, D. Dawson (Ottawa) 13 Sep -- 24 Sep, G. Greven, C. Kipnis (Paris) 15 Aug -- 15 Sep, R. Martinelli (Rome) 20 Oct -- 20 Nov, E. Olivieri (Rome) 1 Oct -- 30 Nov, E. Perkins (UBC), P. March (Ohio State), J. Shiga (Tokyo) ?1 Sep -- 30 Sep, E. Pardoux (Marseille) 23 Aug -- 17 Sep, M. Aizenman (Princeton) 1 Jul -- 31 Jul, G. BenArous (Orsay), R. Andjel (Marseille) 1 Sep -- 30 Sep

Shorter Visits

Many people have expressed interest in visiting for shorter periods, including the following:

D. Aldous (Berkeley), J. Chayes (UCLA), P. Clifford (Oxford), J. T. Cox (Syracuse), L. Gray (Minneapolis), R. Holley (Colorado), J. Hammersley (Oxford), N. Madras (York, Canada), A. Sznitman (ETH).

Programme

There will be a regular seminar programme throughout the period. As well as a programme of special weeks of concentration on certain topics, there will be symposia as follows:

4--16 July: NATO Advanced Study Institute

Probability Theory of Spatial Disorder and Phase Transition

Exposition and discussion of recent theoretical advances in the rigorous study of spatial random processes, particularly random media and interacting particle systems. Major themes will include aspects of interacting particle processes, random walk, percolation, Gibbs states and phase transition, physical systems (e.g. Ising and Potts models, spin glasses, quantum spin systems), cellular automata, ergodic theory of spatial systems, random media. Various leading researchers will give short tutorial courses on nominated topics, intended for newcomers to the field. There will be opportunities for certain invited participants to give lectures on their work.

The main speakers will include

M. Aizenman, B. Derrida, D. Fisher, D. Griffeath, G. R. Grimmett, M. Keane, G . Lawler, T. M. Liggett, C. M.Newman, G. Papanicolaou, R. H. Schonmann, S. Shlosman, G. Slade.

Individuals seeking invitations, or enquiring about financial support, should contact the ASI Director, Geoffrey Grimmett (address below), as soon as possible and certainly by 15 March 1993.

13--17 September: Symposium entitled:

Stochastic Methods in Partial Differential Equations

At the end of a period of activity on stochastic analysis, lasting from 1--17 September, there will be a symposium devoted to areas within the following topics: stochastic partial differential equations, measure-valued diffusions, stochastic methods in non-linear pde, large deviations.

The main speakers will include

D. Dawson (Carleton), P. Donnelly (QMW), E. Pardoux (Marseille), A. DeMasi (L'Aquila), E. Presutti (Rome), E. Bolthausen (Zurich), and others to be confirmed.

November (perhaps 17--27): Symposium

A symposium on one or two nominated topics such as hydrodynamic limits of interacting processes, and metastability and the Ising model. Part of the symposium may be in the nature of a review of recent progress, and open problems in greater generality.