Interaction and growth in complex stochastic systems

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Programme theme

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

Preprints

Title	Year	Programme
Brownian intersection local times: exponential moments and law of large masses Authors: P Morters, Wolfgang Konig Download PDF	2003	IGS
Mixing and convergence rates for a family of Markov processes approximating SDEs Authors: Alexander Veretennikov, SA Klokov Download PDF	2003	IGS
On ergodic measures for McKean-Vlasov stochastic equations Authors: Alexander Veretennikov Download PDF	2003	IGS
Large deviation in a two-servers system with dynamic routing Authors: Yurii Suhov, ND Vvedenskaya, Eugene Pechersky Download PDF	2003	IGS
Limit theorems for random exponentials Authors: Leonid Bogachev, Stanislav Molchanov, G Ben Arous Download PDF	2003	IGS
On ergodic measures for McKean-Vlasov stochastic equations 2 Authors: Alexander Veretennikov Download PDF	2003	IGS
Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit Authors: B Valko, B Toth Download PDF	2003	IGS
On the origin and the use of fluctuation relations for the entropy Authors: C Maes Download PDF	2003	IGS
Random minimal directed spanning trees and Dickman-type distributions Authors: A Wade, MD Penrose Download PDF	2003	IGS
Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$ Authors: Gordon Slade, Remco Van der Hofstad Download PDF	2003	IGS
Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$: the first three terms Authors: Gordon Slade, Remco Van der Hofstad Download PDF	2003	IGS
Approximation of convex curves by random lattice polygons Authors: SM Zarbaliev, Leonid Bogachev Download PDF	2003	IGS
Normal approximation in geometric probability Authors: MD Penrose, Joseph Yukich Download PDF	2003	IGS
Explosion phenomena in stochastic coagulation- fragmentation models Authors: Wolfgang Wagner Download PDF	2003	IGS
Limit laws for norms of i.i.d. samples with Weibull tails Authors: Leonid Bogachev Download PDF	2003	IGS

Workshops

IGSW01

Seminars

Tuesday 22nd July 2003
14:00 to 15:00	Alexander Bulinski Institute of Mechanics of Moscow State University Statistical variant of the multidimensional central limit theorem for random fields	Room 1

Thursday 24th July 2003
14:00 to 15:00	Michael Goldstein University of Toronto Schrodinger cocycles: Introduction; Lyapunov exponents, integrated density of states, large deviation estimates	Room 1

Tuesday 29th July 2003
14:00 to 15:00	Scaling invariance and inverse cascade in 2D ideal fluid	Room 1

Thursday 31st July 2003
14:00 to 15:00	Mitchell Feigenbaum Rockefeller University Pattern selection and distant boundary data	Room 1

Tuesday 5th August 2003
14:00 to 15:00	Gordon Slade University of British Columbia Random subgraphs of finite graphs	Room 2

Thursday 7th August 2003
14:00 to 15:00	Limit shape theorem for stochastic flows	Room 1

Tuesday 12th August 2003
14:00 to 15:00	One-dimensional KPZ growth and random matrices	Room 1

Thursday 14th August 2003
14:00 to 15:00	Nikolai Makarov CALTECH (California Institute of Technology) Some thoughts on the Schramm-Loewner evolution (SLE)	Room 1
16:00 to 17:00	Stanislav Molchanov Non-stationary Andersen parabolic model	Room 1

Tuesday 26th August 2003
14:00 to 15:00	Krzysztof Burdzy University of Washington Couplings and reflecting Brownian motions	Room 1
16:00 to 17:00	Roberto Fernandez Université de Rouen Birth-and-death processes in random environment	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	Hydrodynamic limits for systems with two conservation laws	Room 1
16:00 to 17:00	Federico Camia EURANDOM Continuum nonsimple loops and 2D critical percolation	Room 1

Tuesday 2nd September 2003
14:00 to 15:00	Thierry Bodineau Stability of interfaces and stochastic dynamics	Room 1
16:00 to 17:00	Is Brownian intersection local time multifractal?	Room 1

Thursday 4th September 2003
14:00 to 15:00	Anton Bovier Technische Universität Berlin Metastability in Kawasaki dynamics	Room 1
16:00 to 17:00	Diffusion in random and deterministic fractal environments	Room 1

Tuesday 9th September 2003
14:00 to 15:00	Pavel Bleher Double scaling limits in random matrix models	Room 1

Thursday 11th September 2003
14:00 to 15:00	Droplet condensation/evaporation in a critical regime	Room 1

Tuesday 23rd September 2003
14:00 to 15:00	Herbert Spohn Technische Universität München 1D growth processes and the 3D Ising model at low temperatures	Room 2

Thursday 25th September 2003
14:00 to 15:00	Friedrich Goetze Asymptotic approximations for spectral distributions	Room 2

Tuesday 30th September 2003
14:00 to 15:00	Robert Minlos Spectral properties of the "birth-death" model	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 Stability of interfaces and stochastic dynamics in the regime of partial wetting	Room 1

Thursday 9th October 2003
14:00 to 15:00	Natalia Tsilevich Steklov Mathematical Institute, Russian Academy of Sciences Poisson-Gauss correspondence and orthogonal decompositions	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 On ergodic measures for McKean-Vlasov equations	Room 1

Tuesday 21st October 2003
16:00 to 17:00	Forest fires and self-organised criticality	Room 1

Thursday 23rd October 2003
14:00 to 15:00	S Shlosman Poisson hypothesis for large information networks	Room 1

Tuesday 28th October 2003
14:00 to 15:00	S Shlosman How flat the flat facets of the crystal are?	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 Contour methods and cluster expansion of Kac Ising models	Room 1
16:00 to 17:00	Some remarks on quantum entropies etc	Room 1

Tuesday 4th November 2003
16:00 to 17:00	Tadahisa Funaki University of Tokyo Zero temperature limit for interacting Brownian particles	Room 1

Thursday 6th November 2003
14:00 to 15:00	Anatoly Vershik Pereslavl-Zalessky of the Russian Academy of Sciences Random matrices and random metric spaces	Room 1

Tuesday 11th November 2003
16:00 to 17:00	Joseph Yukich Lehigh University Random interfaces in ballistic deposition	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 Poisson boundary and entropy for random walks on groups	Room 1

Tuesday 18th November 2003
16:00 to 17:00	George Molchan Aalborg Universitet Unilateral small deviations for some selfsimilar Gaussian processes	Room 1

Thursday 20th November 2003
14:00 to 15:00	Leonid Bogachev University of Leeds Limit laws for sums of random exponentials	Room 1

Tuesday 25th November 2003
16:00 to 17:00	Oliver Penrose Heriot-Watt University Random sequential deposition onto graphs	Room 1

Thursday 27th November 2003
14:00 to 15:00	Eugene Pechersky Pereslavl-Zalessky of the Russian Academy of Sciences Uniqueness criterion for Gibbs fields with non-compact spin-space	Room 1

Tuesday 2nd December 2003
14:00 to 15:00	Positive/negative correlation and random-cluster	Room 1
16:00 to 17:00	Alexander Veretennikov University of Leeds Large deviations and mixing for stochastic differential equations and their approximation schemes	Room 1

Thursday 4th December 2003
14:00 to 15:00	Ostap Hryniv University of Cambridge Critical prewetting: some rigorous results	Room 1

Monday 15th December 2003
14:00 to 15:00	Roland Friedrich Analytic geometric aspects of SLE	Room 1

Wednesday 17th December 2003
14:00 to 15:00	Robert Bauer University of Illinois at Urbana-Champaign Generalised chordal Loewner equation	Room 1

Interaction and growth in complex stochastic systems

Organisers

Erwin Bolthausen ETH Zürich
Kostya Khanin Isaac Newton Institute
Gregory Lawler Cornell University
James Norris University of Cambridge
Yuri Suhov University of Cambridge

Speakers

Robert Bauer University of Illinois at Urbana-Champaign
Pavel Bleher
Thierry Bodineau
Leonid Bogachev University of Leeds
Anton Bovier Technische Universität Berlin
Alexander Bulinski Institute of Mechanics of Moscow State University
Krzysztof Burdzy University of Washington
Federico Camia EURANDOM
Anna Erschler
Mitchell Feigenbaum Rockefeller University
Roberto Fernandez Université de Rouen
Roland Friedrich
Tadahisa Funaki University of Tokyo
Friedrich Goetze
Michael Goldstein University of Toronto
Ostap Hryniv University of Cambridge
Dmitry Ioffe Technion - Israel Institute of Technology
Nikolai Makarov CALTECH (California Institute of Technology)
Robert Minlos
George Molchan Aalborg Universitet
Stanislav Molchanov
Eugene Pechersky Pereslavl-Zalessky of the Russian Academy of Sciences
Oliver Penrose Heriot-Watt University
S Shlosman
Gordon Slade University of British Columbia
Herbert Spohn Technische Universität München
Natalia Tsilevich Steklov Mathematical Institute, Russian Academy of Sciences
Alexander Veretennikov University of Leeds
Anatoly Vershik
Joseph Yukich Lehigh University
Milos Zahradnik Charles University, Prague

Show All

Interaction and growth in complex stochastic systems

Programme theme

Preprints

Brownian intersection local times: exponential moments and law of large masses

Mixing and convergence rates for a family of Markov processes approximating SDEs

On ergodic measures for McKean-Vlasov stochastic equations

Large deviation in a two-servers system with dynamic routing

Limit theorems for random exponentials

On ergodic measures for McKean-Vlasov stochastic equations 2

Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit

On the origin and the use of fluctuation relations for the entropy

Random minimal directed spanning trees and Dickman-type distributions

Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$

Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$: the first three terms

Approximation of convex curves by random lattice polygons

Normal approximation in geometric probability

Explosion phenomena in stochastic coagulation- fragmentation models

Limit laws for norms of i.i.d. samples with Weibull tails

Workshops

Conformal invariance and random spatial processes

Random walks in random environment

Random matrix theory satellite meeting - Gregynog Hall, Wales

Stochastic methods in coagulation and fragmentation

Seminars

Organisers

Speakers

Supported By

Interaction and growth in complex stochastic systems

Programme theme

Preprints

Brownian intersection local times: exponential moments and law of large masses

Mixing and convergence rates for a family of Markov processes approximating SDEs

On ergodic measures for McKean-Vlasov stochastic equations

Large deviation in a two-servers system with dynamic routing

Limit theorems for random exponentials

On ergodic measures for McKean-Vlasov stochastic equations 2

Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit

On the origin and the use of fluctuation relations for the entropy

Random minimal directed spanning trees and Dickman-type distributions

Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$

Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$: the first three terms

Approximation of convex curves by random lattice polygons

Normal approximation in geometric probability

Explosion phenomena in stochastic coagulation- fragmentation models

Limit laws for norms of i.i.d. samples with Weibull tails

Workshops

Conformal invariance and random spatial processes

Random walks in random environment

Random matrix theory satellite meeting - Gregynog Hall, Wales

Stochastic methods in coagulation and fragmentation

Seminars

Organisers

Speakers

Supported By

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