Random walks in random environment

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Workshop theme

Supported by The European Science Foundation (ESF) through its project "Random Dynamics in Spatially Extended Systems"

Much is now known on models of random walks in a symmetric random environment. This leads to a diffusion-type behaviour with effectively a non-random diffusion matrix. The phenomena of effective self-averaging for random walks in a symmetric random environment is closely related to the homogenization problem for second order elliptic operators with random coefficients. Most results in this area were obtained in 1980's. However, the general asymmetric case of a random walk in a random environment cannot be treated by similar techniques, and remains largely open in more than one dimension. There has recently been considerable progress in particular concerning random walks in random environment with ballistic behaviour and large deviation principles for random walks in random environments. But many questions are still open. For instance, it is still not known whether for large enough perturbations one can get non-diffusive behaviour for high dimension. Also, almost nothing is known rigorously in the two-dimensional case.

Of considerable interest are also random walks in a random potentials. Here, if the potential is time independent, the asymptotic behaviour can be non-diffusive, and particles move to a trap where they stay for a long time. At the same time, the important case of a time-dependent potential is much less understood, although there are interesting recent developments.

Some closely related topics are: Random walks in random sceneries, directed polymers in random environments (which are connected with a wide class of growth models), and aging phenomena.

Timetable

Monday 18th August 2003
08:15 to 09:00	Registration	No Room Required
09:00 to 09:45	Martin Barlow University of British Columbia Random walks on percolation clusters	Room 1
10:00 to 10:45	Probabilistic aspects of the 3x+1 problem	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:15	Noam Berger University of California Biased random walk on percolation clusters	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:45	Bernard Derrida Athens University of Economics and Business Universal probability distributions of the free energy of directed polymers in a random medium	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Stanislav Molchanov Non-stationary Anderson models and their applications	Room 1
18:00 to 18:45	Wine \& Beer Reception	No Room Required
18:45 to 19:30	Dinner at Wolfson Court (Residents Only)	No Room Required

Tuesday 19th August 2003
09:00 to 09:45	Carlo Boldrighini Random walks in space-time random environments	Room 1
10:00 to 10:45	Firas Rassoul-Agha Ohio State University Large deviations for random walks in a mixing random environment, and other (non-Markov) random walks	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:15	Tomasz Komorovski Maria Curie Sklodowska University Invariant measures for passive tracer dynamics	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:45	Itai Benjamini University of California, Irvine and Weizmann Institute of Science Few random walks problems	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Martin Zerner Stanford University On excited random walks in random and non-random media	Room 1
16:30 to 17:15	Stu Whittington University of Toronto Polymer adsorption - random copolymers and random surfaces	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents Only)	No Room Required

Wednesday 20th August 2003
09:00 to 09:45	Francis Comets Université Paris 7 - Denis-Diderot Brownian directed polymers in randmom environment	Room 1
10:00 to 10:45	Nobuo Yoshida Kyoto University Localisation transition of friendly walkers	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:15	Philippe Carmona Université de Nantes Fluctuation exponents and large deviations for directed polymers in a random environment	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:45	Modified regeneration times for RWRE	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Lingering random walks in dimension one	Room 1
16:30 to 17:15	Random Schroedinger operators with scaled Gibbsian potentials	Room 1
20:00 to 00:00	Conference Dinner at Magdalene College	No Room Required

Thursday 21st August 2003
09:00 to 09:45	Vladas Sidoravicius IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro Percolation in dependent environment	Room 1
10:00 to 10:45	Some proofs for Vertex-reinforced jump processes ("Werner Walks")	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:15	Heinrich Matzinger Recovering information from a randomly mixed up message-text	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:45	Intermittency in a catalytic random medium	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Decay of the return probability for symmetric RWRE	Room 1
16:30 to 17:15	Joseph Conlon University of Michigan Homogenisation of random walk in asymmetric random environment	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents Only)	No Room Required

Friday 22nd August 2003
09:00 to 09:45	Barry Hughes University of Melbourne Stochastically evolving networks	Room 1
10:00 to 10:45	Dmitry Ioffe Technion - Israel Institute of Technology Random walk representation and fluctuation theory of phase separation lines	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:15	Nina Gantert Spending its life at the bottom: the local time of recurrent RWRE	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:45	Thierry Delmotte Université Paul Sabatier Toulouse III Estimates for random walks in symmetric random environment applied to stochastic interface	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Oleg Zaboronski University of Warwick Survival probability of a test particle in a random vicious environment	Room 1
16:30 to 17:15	Harry Kesten Cornell University Some particle systems with moving catalysts	Room 1
18:45 to 19:30	Dinner at Wolfson Court (Residents Only)	No Room Required

Speakers

Martin Barlow University of British Columbia
Itai Benjamini University of California, Irvine and Weizmann Institute of Science
Noam Berger University of California
Carlo Boldrighini
Philippe Carmona Université de Nantes
Francis Comets Université Paris 7 - Denis-Diderot
Joseph Conlon University of Michigan
Thierry Delmotte Université Paul Sabatier Toulouse III
Bernard Derrida Athens University of Economics and Business
Nina Gantert
Barry Hughes University of Melbourne
Dmitry Ioffe Technion - Israel Institute of Technology
Harry Kesten Cornell University
Tomasz Komorovski Maria Curie Sklodowska University
Heinrich Matzinger
Stanislav Molchanov
Firas Rassoul-Agha Ohio State University
Vladas Sidoravicius IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro
Stu Whittington University of Toronto
Nobuo Yoshida Kyoto University
Oleg Zaboronski University of Warwick
Martin Zerner Stanford University

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