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Lectures on Probability Theory and Statistics : Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 / / by Boris Tsirelson, Wendelin Werner ; edited by Jean Picard



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Autore: Tsirelson Boris Visualizza persona
Titolo: Lectures on Probability Theory and Statistics : Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 / / by Boris Tsirelson, Wendelin Werner ; edited by Jean Picard Visualizza cluster
Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004
Edizione: 1st ed. 2004.
Descrizione fisica: 1 online resource (VIII, 200 p.)
Disciplina: 519.2
Soggetto topico: Probabilities
Statistical physics
Dynamical systems
Probability Theory and Stochastic Processes
Complex Systems
Statistical Physics and Dynamical Systems
Soggetto non controllato: Probability theory
Classificazione: 31.70
31.73
Persona (resp. second.): WernerWendelin
PicardJean
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di contenuto: Preface -- Part I: Boris Tsirelson: Scaling Limit, Noise, Stability -- Introduction -- A First Look -- Abstract Nonsense of the Scaling Limit -- Scaling Limit and Independence -- Example: The Noise Made by a Poison Snake -- Stability -- Generalizing Wiener Chaos -- Example: The Brownian Web as a Black Noise -- Miscellany -- References -- Index -- Part II: Wendelin Werner: Random Planar Curves and Schramm-Loewner Evolutions -- Introduction -- Loewner Chains -- Chordal SLE -- Chordal SLE and Restriction -- SLE and the Brownian Frontier -- Radial SLE -- Some Critical Exponents for SLE -- Brownian Exponents -- SLE, UST and LERW -- SLE and Critical Percolation -- What is Missing -- References.
Sommario/riassunto: This is yet another indispensable volume for all probabilists and collectors of the Saint-Flour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some two-dimensional random curves. It provides a definition and properties of the Schramm-Loewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees.
Titolo autorizzato: Lectures on Probability Theory and Statistics  Visualizza cluster
ISBN: 3-540-39982-8
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910767588003321
Lo trovi qui: Univ. Federico II
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Serie: École d'Été de Probabilités de Saint-Flour, . 0721-5363 ; ; 1840