Mathematical statistical physics : Ecole d'Ete de Physique des Houches : Session LXXXII : 4-29 July, 2005 : ESF Summer School : Ecole thematique du CNRS / / edited by Anton Bovier ... [et al.]

• Record Nr.: UNINA9911139757703321
• Pubbl/distr/stampa: Amsterdam ; ; London, : Elsevier, c2006
• ISBN: 1-281-05239-6; 9786611052393; 0-08-047923-5
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (849 p.)
• Collana: Les Houches
• Altri autori (Persone): BovierAnton <1957->
• Disciplina: 530.15
• Soggetti: Mathematical physics; Statistical mechanics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Front cover; Lecturers who contributed to this volume; Title page; Copyright page; Previous sessions; Organizers; Lecturers; Participants; Preface; Informal seminars; Table of contents; Course 1 Random matrices and determinantal processes; Introduction; Point processes; General theory; Determinantal processes; Measures defined by products of several determinants; Non-intersecting paths and the Aztec diamond; Non-intersecting paths and the LGV theorem; The Aztec diamond; Relations to other models; Asymptotics; Double contour integral formula for the correlation kernel; Asymptotics for the Aztec diamondAsymptotics for random permutations; The corner growth model; Mapping to non-intersecting paths; The Schur and Plancherel measures; A discrete polynuclear growth model; Proof of theorem 5.1; References; Course 2 Some recent aspects of random conformally invariant systems; Some discrete models; Self-avoiding walks and polygons; Random walk loops; Site-percolation; The Ising model; The Potts models; FK representations of Potts models; The O(N) models; Conformal invariance; A ""conformal Haar measure"" on self-avoiding loops; Preliminaries; A conformal invariance propertyUniqueness; Existence; Schramm-Loewner Evolutions; Definition; Computing with SLE; Conformal loop-; ensembles; Definition; First properties; The loop-soup construction; The Gaussian free field; Definition; ""Cliffs"" as level lines; References; Course 3 Conformal random geometry; Preamble; Introduction; A brief conformal history; Conformal geometrical structures; Quantum gravity; Stochastic Löwner evolution; Recent developments; Synopsis; Intersections of random walks; Non-intersection probabilities; Quantum gravity; Random walks on a random lattice; Non-intersections of packets of walksMixing random & self-avoiding walks; General star configurations; Quantum gravity for SAW's & RW's; RW-SAW exponents; Brownian hiding exponents; Percolation clusters; Cluster hull and external perimeter; Harmonic measure of percolation frontiers; Harmonic and path crossing exponents; Quantum gravity for percolation; Multifractality of percolation clusters; Conformally invariant frontiers and quantum gravity; Harmonic measure and potential near a fractal frontier; Calculation of multifractal exponents from quantum gravity; Geometrical analysis of multifractal spectraHigher multifractal spectra; Double-sided spectra; Higher multifractality of multiple path vertices; Winding of conformally invariant curves; Harmonic measure and rotations; Exact mixed multifractal spectra; Conformal invariance and quantum gravity; Rotation scaling exponents; Legendre transform; O(N) & Potts models and the Stochastic Löwner Evolution; Geometric duality in O(N) and Potts cluster frontiers; Geometric duality of SLEkappa; Quantum gravity duality and SLE; Dual dimensions; KPZ for SLE; Short distance expansion; Multiple paths in O(N), Potts models and SLE
• Sommario/riassunto: The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians.· introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science· roadmap to the next decade of mathematical statistical mechanics· volume for reference years to come