École d'Été de Probabilités de Saint-Flour

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Saint-Flour

The École d'Été de Probabilités de Saint-Flour (English: Probability Summer School Saint-Flour ) is an annual summer school for probability theory and statistics at the University of Clermont-Ferrand and takes place in Saint-Flour . It is the world's most renowned course in this field. It is organized by the Laboratoire de Mathématiques Blaise Pascal (LMBP, UMR 6620) of the University of Clermont-Ferrand and the CNRS , supported by the European Mathematical Society . It is aimed at doctoral students and scientists in the field and is at an advanced level. There are usually three main courses. The lectures are published in Springer's Lecture Notes in Mathematics (LNM). They have also been online on YouTube since 2018 . In addition to the courses, there are shorter lectures and lectures as well as posters in which the participants can present their research, scientific exchange and discussions. The summer school usually takes place around two and a half weeks in July, but also took place in August / early September and was already three weeks long.

There are up to 100 participants. The speakers are selected by an international committee of scientists, most of whom have already held summer courses there, and are usually determined two years in advance. The course lectures usually take place in the morning, presentations in the early afternoon.

history

The seminar was founded at a time of reform and rapid expansion of French universities. The assistants and lecturers wanted to invite internationally known scientists for active research, which was the ideal summer break, during which the families could accompany the participants. Accordingly, the atmosphere was initially very familiar, but this was later increasingly pushed back. Because of the heat in Clermont-Ferrand in July , they wanted to move to a nearby mountain village (altitude 900 m) and chose the Maison des Planchettes in Saint-Flour, which was a training center for priests until the 1950s and was then used as a home. A neighboring chapel and an old library remind of the past of the 18th century building. The first summer school with 36 participants was organized by the mathematics professors in Clermont-Ferrand Paul-Louis Hennequin (* 1930) and Albert Badrikian (1933–1994). The latter was the driving force in the initial phase, organized the Sunday excursions and had a fatal accident in 1994 shortly after the summer school on the Bosson Glacier . Hennequin and Valerian were assisted by Jacques Neveu in Paris, an influential proponent of the renewal of stochastics in France after World War II, who had a great influence on the summer school in the early years. Due to his influence, the summer school in 1976 is said to have been set for the end of August, as he only had time then. But now it always takes place in July. After Hennequin, Pierre Bernard was the organizer and, from 2011, Jean Picard .

Only Xavier Fernique and Paul-André Meyer held two courses in the early years; later, each speaker was only allowed to hold one course in the course of his career. Among the lecturers (as of 2019) are three Fields medalists ( Cédric Villani (lecture 2005, Fields medal 2010), Wendelin Werner (lecture 2002, Fields medal 2006), Martin Hairer (Fields medal 2014, previously held in the same year he gave his lecture in Saint-Flour)), one received the Abel Prize ( SRS Varadhan ), and almost all the recipients of the Loève Prize are represented (except Oded Schramm and Alexei Borodin ), a total of eleven by 2019.

In 2020 the organizing committee is: Christophe Bahadoran, Arnaud Guillin, Hacène Djellout.

Directory of courses

If they have been published, the publication - usually Lecture notes in mathematics (LNM) - and the page number are given.

  • 1971 (No. I): Jean Bretagnolle , Processus a accroissements indépendants (LNM 307, Springer 1973, pp. 1–26), Srishti Dhar Chatterji (1935–2017), Les martingales et leurs applications analytiques (LNM 307, p. 27 –164), Paul-André Meyer , Présentation des processus de Markov (LNM 307, pp. 165–198), Claude Dellacherie , Théorie générale des processus.
  • 1972 (No. II): Serge Dubuc , Processus en cascade, Gopinath Kallianpur : Processus gaussiens et questions annexes, JP Keane: Transformations ergodiques des espaces de probabilité.
  • 1973 (No. III, LNM 390, Springer 1974): Paul-André Meyer , Transformation des processus de Markov (pp. 1-36), Pierre Priouret , Processus de diffusion et equations différentielles stochastiques (pp. 37-113), Frank L. Spitzer , Introduction aux processus de Markov a paramètre dans (pp. 114–189)
  • 1974 (No. IV, LNM 480, Springer 1975): Xavier Fernique , Régularité des trajectoires des fonctions aléatoires gaussiennes (pp. 1–96), Jean-Pierre Conze , Systemes topologiques et métriques en théorie ergodique (pp. 97–187) , Joe Gani , Processus stochastiques de population (notes rédigées par Mme. J. Badrikian) (pp. 189–293)
  • 1975 (No. V, LNM 539, Springer 1976): Albert Badrikian , Prolégomènes au calcul des probabilités dans les Banach (pp. 1–166), John Frank Charles Kingman , Subadditive processes (pp. 167–223), James Kuelbs , The law of the iterated logarithm and related strong convergence theorems for Banach space valued random variables (pp. 224–314)
  • 1976 (No. VI, LNM 598, Springer 1977): Jørgen Hoffmann-Jørgensen , Probability in Banach space (pp. 1-186), Thomas M. Liggett , The stochastic evolution of infinite systems of interacting particles (pp. 187-248 ), Jacques Neveu , Processus ponctuels (pp. 249–445)
  • 1977 (no. VII, LNM 678, Springer 1978): Didier Dacunha-Castelle , Vitesse de convergence pour certainsproblemèmes statistiques (pp. 1–172), Herbert Heyer , Semigroupes de convolution sur un groupe localement compact et applications a la théorie des probabilités (pp. 173–236), Bernard Roynette , Marches aléatoires sur les groupes de Lie (pp. 237–379)
  • 1978 (No. VIII, LNM 774, Springer 1980): Robert Azencott , Grandes déviations et applications (pp. 1-176), Yves Guivarc'h , Quelques propriétés asymptotiques des produits de matrices aléatoires (pp. 177-250), Richard Gundy , Inégalités pour martingales à un et deux indices: l'espace (pp. 251–334)
  • 1979 (No. IX, LNM 876, Springer, 1981): Peter John Bickel , Quelques aspects de la statistique robust (pp. 1–72), Nicole El Karoui : Les aspects probabilistes du contrôle stochastique (pp. 73–238), Marc Yor , Sur la théorie du filtrage (pp. 239–280)
  • 1980 (No. X, LNM 929, Springer, 1982): Jean-Michel Bismut , Mécanique aléatoire (p. 1–100), Leonard Gross , Thermodynamics, statistical mechanics and random fields (p. 101–204), Klaus Krickeberg , Processus ponctuels en statistique (205–313)
  • 1981 (No. XI, LNM 976, LNM 1007, Springer 1983): Xavier Fernique , Régularité de fonctions aléatoires non gaussiennes (pp. 1-74), P. Warwick Millar , The minimax principle in asymptotic statistical theory (pp. 75– 265), Daniel W. Stroock , Some applications of stochastic calculus to partial differential equations (pp. 267–382), M. Weber, Analyze infinitésimale de fonctions aléatoires (pp. 383–465)
  • 1982 (No. XII, LNM 1097, Springer, 1984), Richard Mansfield Dudley , A course on empirical processes (pp. 1–142), Hiroshi Kunita , Stochastic differential equations and stochastic flows of diffeomorphisms (pp. 143–303), François Ledrappier , Quelques propriétés des exposants caractéristiques (pp. 305–396)
  • 1983 (No. XIII, LNM 117, Springer 1985): David J. Aldous , Exchangeability and related topics (pp. 1–198), Ildar Abdulowitsch Ibragimow , Théorèmes limites pour les marches aléatoires (pp. 199–297), Jean Jacod , Théorèmes limit pour les processus (pp. 298–409)
  • 1984 (No. XIV, LNM 1180, Springer 1986): René Carmona , Random Schrödinger operators (pp. 1-124), Harry Kesten , Aspects of first passage percolation (pp. 125-264), John B. Walsh , An introduction to stochastic partial differential equations (pp. 265–439)
  • 1985 (No. XV): Pierre Cartier , Méthodes d'analysis non standard en probabilité, SR Srinivasa Varadhan , Large deviations and applications (LNM 1362, Springer 1988, pp. 1-49), Persi Diaconis , Applications of noncommutative Fourier analysis to probability problems (LNM 1362, pp. 51-100),
  • 1986 (No. XVI), Ole Barndorff-Nielsen , Parametric statistical models and likelihood (Lecture Notes in Statistics 50, Springer 1988), Hans Föllmer , Random fields and diffusion processes (LNM 1362, Springer 1988, pp. 101-203), George C. Papanicolaou , Waves in one-dimensional random media (LNM 1362, pp. 205–275),
  • 1987 (No. XVII): David Elworthy , Geometric aspects of diffusions on manifolds (LNM 1362, Springer 1988, pp. 277-425), Edward Nelson , Stochastic mechanics and random fields (LNM 1362, pp. 427-450), Laure Elie , Marches aléatoires et fonctions harmoniques.
  • 1988 (No. XVIII, LNM 1427, Springer, 1990): Alano Ancona , Théorie du potentiel sur les graphes et les variétés (pp. 1-112), Donald Geman , Random fields and inverse problems in imaging (pp. 113-193 ), Nobuyuki Ikeda , Probabilistic methods in the study of asymptotics (pp. 195–325)
  • 1989 (No. XIX, LNM 1464, Springer, 1991): Donald Burkholder , Explorations in martingale theory and its applications (pp. 1–66), Etienne Pardoux , Filtrage non linéaire et équations aux dérivées partielles stochastiques associées (p. 67– 163), Alain-Sol Sznitman , Topics in propagation of chaos (pp. 165-251).
  • 1990: Mark Iossifowitsch Freidlin , Semi-linear PDEs and limit theorems for large deviations (LNM 1527, Springer, 1992, pp. 1–109), Jean-François Le Gall , Some properties of planar Brownian motion (LNM 1527, p. 111 -235), David Donoho , Function estimation and the white noise model.
  • 1991 (LNM 1541, Springer, 1993): Donald A. Dawson , Measure-valued Markov processes (pp. 1-260), Bernard Maisonneuve , Processus de Markov: naissance, retournement, régénération (pp. 261-292), Joel Spencer , Nine lectures on random graphs (pp. 293–347)
  • 1992 (LNM 1581, Springer, 1994): Dominique Bakry , L'hypercontractivité et son utilization en théorie des semigroupes (pp. 1–114), Richard D. Gill , Lectures on survival analysis (pp. 115–241), Stanislaw Alexejewitsch Moltschanow , Lectures on random media (pp. 242–411)
  • 1993: Philippe Biane , Calcul stochastique non-commutatif (LNM 1608, Springer, 1995, pp. 1-96), Rick Durrett , Ten lectures on particle systems (LNM 1608, pp. 97-201), Richard M. Karp , Probabilistic algorithms in computer science.
  • 1994 (LNM 1648, Springer, 1996): Roland Lwowitsch Dobruschin (Dobrushin), Perturbation methods of the theory of Gibbsian fields (pp. 1-66), Piet Groeneboom , Lectures on inverse problems (pp. 67-164), Michel Ledoux , Isoperimetry and Gaussian analysis (pp. 165–294)
  • 1995: Martin T. Barlow , Diffusions on fractals (LNM 1690, Springer, 1998, pp. 1–121), David Nualart , Analysis on Wiener space and anticipating stochastic calculus (LNM 1690, pp. 123–227), Gérard Ben Arous , Méthode de Laplace et grandes déviations.
  • 1996 (LNM 1665, Springer, 1997), Evarist Giné , Decoupling and limit theorems for U-statistics and U-processes (pp. 1–35), Evarist Giné, Lectures on some aspects of the bootstrap (pp. 37–151) , Geoffrey Grimmett , Percolation and disordered systems (pp. 153–300), Laurent Saloff-Coste , Lectures on finite Markov chains (pp. 301–413)
  • 1997 (LNM 1717, Springer, 1999): Jean Bertoin , Subordinators: examples and applications (pp. 1-91), Fabio Martinelli , Lectures on Glauber dynamics for discrete spin models (pp. 93-191), Yuval Peres , Probability on trees: an introductory climb (pp. 193–280)
  • 1998 (LNM 1738, Springer, 2000): Michel Emery , Martingales continues dans les variétés différentiables. (Pp. 1–84), Arkadi Nemirovski , Topics in non-parametric statistics (pp. 85–277), Dan Voiculescu , Lectures on free probability theory (pp. 279–349)
  • 1999 (LNM 1781, Springer, 2002): Erwin Bolthausen , Large deviations and Interacting Random Walks (pp. 7-124), Edwin A. Perkins , Dawson-Watanabe superprocesses and Measured-valued Diffusions (pp. 125-329), Aad van der Vaart , Semiparametric Statistics (pp. 331–457)
  • 2000 (LNM 1816, Springer, 2003): Sergio Albeverio , Theory of Dirichlet forms and applications (pp. 1–106), Walter Schachermayer , Introduction to the mathematics of financial markets (pp. 107–179), Michel Talagrand , Mean field models for spin glasses: a first course (pp. 181–285)
  • 2001: Simon Tavaré , Ancestral inference in population genetics (LNM 1837, Springer 2004, pp. 1–188), Ofer Zeitouni , Random walks in random environment (LNM 1837, pp. 189–312), Olivier Catoni , Statistical learning theory and stochastic optimization (LNM 1851, Springer 2004),
  • 2002: Boris Tsirelson , Scaling limit, noise, stability (LNM 1840, Springer 2004, pp. 1–106), Wendelin Werner , Random planar curves and Schramm-Loewner evolutions (LNM 1840, pp. 107–195), Jim Pitman , Combinatorial stochastic processes (LNM 1875, Springer, 2006).
  • 2003: Amir Dembo , Favorite points, cover times and fractals (LNM 1869, Springer 2005, pp. 1–101), Tadahisa Funaki , Stochastic interface models (LNM 1869, pp. 103–274), Pascal Massart , Concentration inequalities and model selection (LNM 1896, Springer 2007),
  • 2004 Raphaël Cerf , The Wulff crystal in Ising and percolation models (LNM 1878, Springer, 2006), Gordon Slade , The lace expansion and its applications (LNM 1879, Springer, 2006), Terry Lyons , Michael J. Caruana and Thierry Lévy , Differential equations driven by rough paths (LNM 1908, Springer, 2007, lecturer was Lyons).
  • 2005 Ronald A. Doney , Fluctuation theory for Lévy processes (LNM 1897, Springer, 2007), Steven N. Evans , Probability and real trees (LNM 1920, Springer, 2008), Cédric Villani , Optimal transport, old and new ( Grundlehren der mathematical sciences , 338, Springer, 2009).
  • 2006 Maury Bramson , Stability of queuing networks (LNM 1950, Springer 2008), Alice Guionnet , Large random matrices: Lectures on macroscopic asymptotics (LNM 1957, Springer, 2009).
  • 2007 Frank den Hollander , Random polymers (LNM 1974, Springer 2009), Jérôme Buzzi , Hyperbolicity through entropies for dynamical systems, Jonathan Mattingly , Ergodicity of stochastic partial differential equations.
  • 2008 Vladimir Koltchinskii , Oracle inequalities in empirical risk minimization and sparse recovery problems (LNM 2033, Springer 2011), Yves Le Jan , Markov paths, loops and fields (LNM 2026, Springer 2011), Richard Kenyon , Dimers and random surfaces.
  • 2009: Alison Etheridge , Some mathematical models from population genetics (LNM 2012, Springer 2011), Robert Adler , Jonathan Taylor , Topological complexity of smooth random functions (LNM 2019, Springer 2011)
  • 2010 (No. XL): Franco Flandoli , Random perturbation of PDEs and fluid dynamic models (LNM 2015, Springer 2011), Giambattista Giacomin , Disorder and critical phenomena through basic probability models (LNM 2025, Springer 2011), Takashi Kumagai , Random walks on disordered media and their scaling limits (LNM 2101).
  • 2011: Itai Benjamini , Coarse geometry and randomness (LNM 2100), Emmanuel Candès , The power of convex relaxation: the surprising stories of compressed sensing and matrix completion, Gilles Schaeffer , Enumerative and bijective combinatorics for random walks, trees and planar maps.
  • 2012: Jeremy Quastel , The KPZ equation and its universality class, Zhan Shi , Branching random walks (LNM 2151), Jeffrey E. Steif , Noise sensitivity and percolation.
  • 2013 (No. XLIII): Krzysztof Burdzy , Brownian motion and its applications to mathematical analysis (LNM 2106), Andrea Montanari , Statistical mechanics on random graphs, Alexandre Tsybakov , Aggregation and high-dimensional statistics.
  • 2014 Martin Hairer , Regularity structures, Grégory Miermont : Aspects of random maps
  • 2015 Sourav Chatterjee : Large deviations for random graphs (LNM 2197), Sara van de Geer , Theory of high-dimensional statistics (LNM 2159), Lorenzo Zambotti , Random obstacle problems (LNM 2181)
  • 2016 Paul Bourgade , Large random matrices, microscopic asymptotics, Francis Comets , Directed polymers in random environments (LNM 2175), Scott Sheffield , Jason P. Miller , Universal randomness in 2 D.
  • 2017 Thierry Bodineau , Large scale dynamics of dilute gases, Remco van der Hofstad , Stochastic processes on random graphs, Gábor Lugosi , Elements of combinatorial statistics
  • 2018 Hugo Duminil-Copin , Lattice spin models in low dimension, Asaf Nachmias , Planar maps, random walks and the circle packing problem, Bálint Tóth , Scaling limit for random walks and diffusion with long memory
  • 2019 Nicolas Curien : Random discrete surfaces, Elchanan Mossel , Probabilistic aspects of voting, intransitivity and manipulation, Philippe Rigollet : Statistical optimal transport.
  • 2020 (No. L, i.e. fiftieth summer school): Ivan Corwin (Columbia University), Integrable probability and Gibbsian line ensembles, Sylvie Méléard (École Polytechnique): The interplay between scales in mathematical modeling for ecology and evolution, Allan Sly (Princeton University) , Random Constraint Satisfaction Problems.

literature

Web links

  • Official website (with a list of courses up to 2018 in pdf and courses 2020, accessed on June 6, 2020)

Individual evidence

  1. ↑ There are two universities. After the LNM volume No. 2243 with the lectures by Nachmias 2018, it is the University of Auvergne Clermont-Ferrand I. In the LNM volume of the 2011 lectures, it was still the University of Blaise-Pascal
  2. ^ Year 2000 European Mathematical Society Saint Flour Summer School On Probability Theory , Cordis, EU
  3. ↑ Website at Springer Verlag
  4. ↑ LNM No. 2243 on the course of Nachmias 2018 specifies a duration of 12 days from 2005, before that it was 17 days.
  5. ^ Jean Picard, LNM-Band for the Summer School 2011
  6. ↑ a b Laurent Serlet, L'École de Probabilités de Saint Flour , Revue Mathématiques en auvergne, Part 1, Revue d'Auvergne, 2014, pp. 217-225
  7. ↑ Werner, Random planar curves and Schramm-Loewner evolutions , Arxiv 2003
  8. ^ Le Jan, Markov paths, loops, fields, Arxiv 2008
  9. ^ Nachmias, Planar maps, random walks and the circle packing problem, Arxiv 2018
  10. ↑ email circular from the organizers 2019