IGS
21 July 2003 to 19 December 2003
Random processes are often understood by means of an asymptotic in which the number of basic random components becomes large. Classical examples of behaviour which can be manifest in such a limit are the law of large numbers and the central limit theorem. These two examples apply in contexts where the interaction between typical random components becomes negligible in the limit. However, there are many extremely important physical models, where such an asymptotic decorrelation does not hold. Such models correspond to a critical behaviour where interaction is strong and statistical scaling properties are highly nontrivial. Understanding of asymptotic properties for such systems is one of the most important problems in the modern probability theory. Renormalization group ideology which was developed by physicists in the last 30 years predicts appearance of the universal scaling and conformal invariant random fields characterizing statistical behaviour in critical situations. However, rigorous results in this direction were out of reach until very recently.
The programme will focus on problems from a number of contexts where strong random interactions give rise to non-classical limiting behaviour. These will include random walk in a random environment and interactive random walk, interfaces in growth models and equilibrium statistical mechanics, coagulation and fragmentation, conformally invariant scaling limits, random matrices.
Powerful new techniques are beginning to make possible the computation of exact asymptotics along with a rigorous understanding of convergence. The range of possible limiting behaviour is rich and introduces to probability new connections with other areas of mathematics and physics. The programme will bring together many aspects of this work, including its applications, from statistical mechanics to applied probability.
Click here to download the programme's final scientific report
Title | Year | Programme | |
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Brownian intersection local times: exponential moments and law of large massesAuthors: P Morters, Wolfgang Konig |
2003 | IGS | 21 October 2016 |
Mixing and convergence rates for a family of Markov processes approximating SDEsAuthors: Alexander Veretennikov, SA Klokov |
2003 | IGS | 21 October 2016 |
On ergodic measures for McKean-Vlasov stochastic equationsAuthors: Alexander Veretennikov |
2003 | IGS | 21 October 2016 |
Large deviation in a two-servers system with dynamic routingAuthors: Yurii Suhov, ND Vvedenskaya, Eugene Pechersky |
2003 | IGS | 21 October 2016 |
Limit theorems for random exponentialsAuthors: Leonid Bogachev, Stanislav Molchanov, G Ben Arous |
2003 | IGS | 21 October 2016 |
On ergodic measures for McKean-Vlasov stochastic equations 2Authors: Alexander Veretennikov |
2003 | IGS | 21 October 2016 |
Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limitAuthors: B Toth, B Valko |
2003 | IGS | 21 October 2016 |
On the origin and the use of fluctuation relations for the entropyAuthors: C Maes |
2003 | IGS | 21 October 2016 |
Random minimal directed spanning trees and Dickman-type distributionsAuthors: A Wade, MD Penrose |
2003 | IGS | 21 October 2016 |
Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$Authors: Gordon Slade, Remco Van der Hofstad |
2003 | IGS | 21 October 2016 |
Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$: the first three termsAuthors: Gordon Slade, Remco Van der Hofstad |
2003 | IGS | 21 October 2016 |
Approximation of convex curves by random lattice polygonsAuthors: SM Zarbaliev, Leonid Bogachev |
2003 | IGS | 21 October 2016 |
Normal approximation in geometric probabilityAuthors: MD Penrose, Joseph Yukich |
2003 | IGS | 21 October 2016 |
Explosion phenomena in stochastic coagulation- fragmentation modelsAuthors: Wolfgang Wagner |
2003 | IGS | 21 October 2016 |
Limit laws for norms of i.i.d. samples with Weibull tailsAuthors: Leonid Bogachev |
2003 | IGS | 21 October 2016 |
7 July 2003 to 18 July 2003
17 August 2003 to 23 August 2003
14 September 2003 to 19 September 2003
7 December 2003 to 13 December 2003
Tuesday 22nd July 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Alexander Bulinski Institute of Mechanics of Moscow State University |
Room 1 |
Thursday 24th July 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Michael Goldstein University of Toronto |
Room 1 |
Tuesday 29th July 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Thursday 31st July 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Mitchell Feigenbaum Rockefeller University |
Room 1 |
Tuesday 5th August 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Gordon Slade University of British Columbia |
Room 2 |
Thursday 7th August 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Tuesday 12th August 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Thursday 14th August 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Nikolai Makarov CALTECH (California Institute of Technology) |
Room 1 | |
16:00 to 17:00 |
Stanislav Molchanov |
Room 1 |
Tuesday 26th August 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Krzysztof Burdzy University of Washington |
Room 1 | |
16:00 to 17:00 |
Roberto Fernandez Université de Rouen |
Room 1 |
Wednesday 27th August 2003 | |||
---|---|---|---|
15:00 to 16:00 |
Distribution of potential near a random conformally invariant curve |
Room 1 |
Thursday 28th August 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | ||
16:00 to 17:00 |
Federico Camia EURANDOM |
Room 1 |
Tuesday 2nd September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Thierry Bodineau |
Room 1 | |
16:00 to 17:00 | Room 1 |
Thursday 4th September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Anton Bovier Technische Universität Berlin |
Room 1 | |
16:00 to 17:00 | Room 1 |
Tuesday 9th September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Pavel Bleher |
Room 1 |
Thursday 11th September 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Tuesday 23rd September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Herbert Spohn Technische Universität München |
Room 2 |
Thursday 25th September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Friedrich Goetze |
Room 2 |
Tuesday 30th September 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Robert Minlos |
Room 1 |
Thursday 2nd October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
On a non-hierarchical version of the generalised random energy model |
Room 1 |
Tuesday 7th October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Dmitry Ioffe Technion - Israel Institute of Technology |
Room 1 |
Thursday 9th October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Natalia Tsilevich Steklov Mathematical Institute, Russian Academy of Sciences |
Room 1 |
Tuesday 14th October 2003 | |||
---|---|---|---|
16:00 to 17:00 |
Variational analysis for functionals of measures and Poisson random fields |
Room 1 |
Thursday 16th October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Alexander Veretennikov University of Leeds |
Room 1 |
Tuesday 21st October 2003 | |||
---|---|---|---|
16:00 to 17:00 | Room 1 |
Thursday 23rd October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
S Shlosman |
Room 1 |
Tuesday 28th October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
S Shlosman |
Room 1 | |
16:00 to 17:00 |
First-order transitions for models with continous symmetries |
Room 1 |
Thursday 30th October 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Milos Zahradnik Charles University, Prague |
Room 1 | |
16:00 to 17:00 | Room 1 |
Tuesday 4th November 2003 | |||
---|---|---|---|
16:00 to 17:00 |
Tadahisa Funaki University of Tokyo |
Room 1 |
Thursday 6th November 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Anatoly Vershik Pereslavl-Zalessky of the Russian Academy of Sciences |
Room 1 |
Tuesday 11th November 2003 | |||
---|---|---|---|
16:00 to 17:00 |
Joseph Yukich Lehigh University |
Room 1 |
Thursday 13th November 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Renovation and limit theorems for a class of stochastic ordered graphs |
Room 1 | |
16:00 to 17:00 |
Anna Erschler |
Room 1 |
Tuesday 18th November 2003 | |||
---|---|---|---|
16:00 to 17:00 |
George Molchan Aalborg Universitet |
Room 1 |
Thursday 20th November 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Leonid Bogachev University of Leeds |
Room 1 |
Tuesday 25th November 2003 | |||
---|---|---|---|
16:00 to 17:00 |
Oliver Penrose Heriot-Watt University |
Room 1 |
Thursday 27th November 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Eugene Pechersky Pereslavl-Zalessky of the Russian Academy of Sciences |
Room 1 |
Tuesday 2nd December 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | ||
16:00 to 17:00 |
Alexander Veretennikov University of Leeds |
Room 1 |
Thursday 4th December 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Ostap Hryniv University of Cambridge |
Room 1 |
Monday 15th December 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Roland Friedrich |
Room 1 |
Wednesday 17th December 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Robert Bauer University of Illinois at Urbana-Champaign |
Room 1 |
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