CONFERENCE
Probabilistic techniques for random and time-varying dynamical systems
Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps
3 - 7 October 2022
Probabilistic techniques for random and time-varying dynamical systems
Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps
3 - 7 October 2022
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Scientific Committee
Comité scientifique Dmitry Dolgopyat (University of Maryland) Carlangelo Liverani (Tor Vergata University of Rome) Lai-Sang Young (New York University) |
Organizing Committee
Comité d'organisation Wael Bahsoun (Loughborough University) Mark Demers (Fairfield University) Matthew Nicol (University of Houston) Françoise Pène (Université de Brest) Mark Pollicott (University of Warwick) |
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Description
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Dynamical systems is a field of mathematics concerned with studying phenomena that evolve over time. It has deep connections with many areas of mathematics such as analysis, geometry, probability and statistics. Traditionally, a dynamical system is modelled either by iterates of a deterministic map or by an autonomous flow preserving a probability measure. Despite the fact that the dynamics is deterministic, many dynamical systems are chaotic in nature and enjoy similarities with purely random models. One of the current challenges in dynamical systems research is to better understand random and time-varying dynamical systems, in particular to develop novel probabilistic techniques to predict their statistical behavior. This direction of research, the ambition of which is to approach more the real by taking in account a time dependence inherent in some phenomena, has recently seen an enormous amount of activity. Many difficulties and questions emerge from this time dependence. Let us mention for example the existence of many open questions about the establishment of quenched limit theorems (the evolution of the dynamics being fixed) for systems with random dynamics. The study of these systems opens new interplays between probability theory and dynamical systems, and leads to interesting insights in other areas of science. The purpose of this conference is to bring together experts and early career researchers from dynamical systems and probability theory to present the latest state-of-the-art on this topic, make progress on outstanding problems and conjectures and to set its research agenda for the foreseeable future.
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Les systèmes dynamiques constituent un champ des mathématiques dédié à l'étude de phénomènes évoluant avec le temps. Cette thématique est à l'interface avec différents domaines des mathématiques tels que l'analyse, la géométrie, les probabilités et les statistiques. Traditionnellement un système
dynamique est décrit par les itérées d'une transformation ou par l'action d'un flot préservant une mesure de probabilité. Bien que la dynamique soit déterministe, de nombreux systèmes dynamiques sont de nature chaotique et ont, par bien des aspects, un comportement analogue à celui de modèles purement aléatoires. Un important défi actuel dans la recherche sur les systèmes dynamiques est la compréhension des systèmes dynamiques aléatoires et des systèmes dont la dynamique évolue avec le temps. L'intérêt pour ces modèles, dont l'ambition est de se rapprocher de la complexité du réel en introduisant une dépendance en temps inhérente à certains phénomènes, connaît actuellement un grand essor. Cette dépendance en temps fait émerger de nombreuses difficultés et questions. Mentionnons par exemple l'existence de nombreuses questions ouvertes concernant l'établissement de théorèmes limites "trempés" (l'évolution de la dynamique étant fixée) pour des dynamiques aléatoires. L'étude du comportement statistique de ces systèmes nécessite ainsi le développement de nouvelles techniques probabilistes, créant de nouvelles opportunités d'interactions entre théorie des probabilités et systèmes dynamiques, et d'intéressantes connexions avec d'autres domaines scientifiques. Cette conférence a pour but de réunir des expert-es et des jeunes chercheurs et jeunes chercheuses en systèmes dynamiques et en probabilité, de présenter les avancées les plus récentes dans la thématique, de favoriser les collaborations mathématiques afin de réaliser des progrès marquants sur des questions et conjectures ambitieuses portant sur les systèmes aléatoires et inhomogènes en temps. |
Speakers
Romain Aimino (University of Porto) Stable laws for random dynamical systems
Viviane Baladi (LPSM, Sorbonne Université) Measure of maximal entropy for finite horizon Sinai billiard flows
Alex Blumenthal (Georgia Institute of Technology) Lyapunov exponents of the Navier-Stokes equations
Roberto Castorrini (University of Pisa) Spectral gap of transfer operators for a class of two-dimensional partially hyperbolic systems
Klaudiusz Czudek (Nicolaus Copernicus University of Toruń) Simple symmetric random walks on the circle
Davor Dragičević (University of Rijeka) Quenched linear response for smooth expanding on average cocycles
Gary Froyland (University of New South Wales) Perturbation formulae for quenched random dynamics with applications to open systems and
extreme value theory
Joanna Furno (University of South Alabama) Bounded remainder sets for rotations on finite-dimensional adelic tori
Cecilia Gonzalez-Tokman (University of Queesnland) Lyapunov–Oseledets spectrum for matrix and transfer operator cocycles under perturbations
Sebastien Gouezel (Université de Rennes 1) Minimal distance between random orbits
Yeor Hafouta (Ohio State University) Limit theorems for non-uniformly random expanding maps under explicit conditions
Tobias Jäger (Friedrich Schiller University Jena) Random semi-uniform ergodic theorems and applications to forced systems
Davit Karagulyan (KTH Sweden) Exponential Fermi accelerator
Alexey Korepanov (Loughborough University) Superdiffusive limits for billiards with cusps
Jeroen Lamb (Imperial College London) Quasi-ergodic measures and conditioned Lyapunov exponents
Florence Merlevède (Université Paris-Est Marne-la-Vallée) Rates of convergence in the CLT for non stationary sequences and application to sequential
dynamical systems
Peter Nandori (Yeshiva University) On the mean field limit of stochastic reaction networks
Tanja Isabelle Schindler (University of Vienna) Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical
systems
Dalia Terhesiu (Mathematisch Instituut, University of Leiden) Stable large and local large deviation for dynamical systems
Damien Thomine (Université Paris-Saclay) A probabilistic induction of intermittent maps
Paulo Varandas (Federal University of Bahia & CMUP) Quenched decay of correlations for random tower maps
Romain Aimino (University of Porto) Stable laws for random dynamical systems
Viviane Baladi (LPSM, Sorbonne Université) Measure of maximal entropy for finite horizon Sinai billiard flows
Alex Blumenthal (Georgia Institute of Technology) Lyapunov exponents of the Navier-Stokes equations
Roberto Castorrini (University of Pisa) Spectral gap of transfer operators for a class of two-dimensional partially hyperbolic systems
Klaudiusz Czudek (Nicolaus Copernicus University of Toruń) Simple symmetric random walks on the circle
Davor Dragičević (University of Rijeka) Quenched linear response for smooth expanding on average cocycles
Gary Froyland (University of New South Wales) Perturbation formulae for quenched random dynamics with applications to open systems and
extreme value theory
Joanna Furno (University of South Alabama) Bounded remainder sets for rotations on finite-dimensional adelic tori
Cecilia Gonzalez-Tokman (University of Queesnland) Lyapunov–Oseledets spectrum for matrix and transfer operator cocycles under perturbations
Sebastien Gouezel (Université de Rennes 1) Minimal distance between random orbits
Yeor Hafouta (Ohio State University) Limit theorems for non-uniformly random expanding maps under explicit conditions
Tobias Jäger (Friedrich Schiller University Jena) Random semi-uniform ergodic theorems and applications to forced systems
Davit Karagulyan (KTH Sweden) Exponential Fermi accelerator
Alexey Korepanov (Loughborough University) Superdiffusive limits for billiards with cusps
Jeroen Lamb (Imperial College London) Quasi-ergodic measures and conditioned Lyapunov exponents
Florence Merlevède (Université Paris-Est Marne-la-Vallée) Rates of convergence in the CLT for non stationary sequences and application to sequential
dynamical systems
Peter Nandori (Yeshiva University) On the mean field limit of stochastic reaction networks
Tanja Isabelle Schindler (University of Vienna) Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical
systems
Dalia Terhesiu (Mathematisch Instituut, University of Leiden) Stable large and local large deviation for dynamical systems
Damien Thomine (Université Paris-Saclay) A probabilistic induction of intermittent maps
Paulo Varandas (Federal University of Bahia & CMUP) Quenched decay of correlations for random tower maps
SPONSORS
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