LEADER 05409nam 2200697Ia 450 001 9910961433603321 005 20251116191427.0 010 $a1-281-05239-6 010 $a9786611052393 010 $a0-08-047923-5 035 $a(CKB)1000000000357741 035 $a(EBL)294248 035 $a(OCoLC)469589460 035 $a(SSID)ssj0000199187 035 $a(PQKBManifestationID)11954303 035 $a(PQKBTitleCode)TC0000199187 035 $a(PQKBWorkID)10204483 035 $a(PQKB)11651968 035 $a(Au-PeEL)EBL294248 035 $a(CaPaEBR)ebr10186083 035 $a(CaONFJC)MIL105239 035 $a(MiAaPQ)EBC294248 035 $a(PPN)178935530 035 $a(EXLCZ)991000000000357741 100 $a20060901d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical statistical physics $eEcole d'Ete de Physique des Houches : Session LXXXII : 4-29 July, 2005 : ESF Summer School : Ecole thematique du CNRS /$fedited by Anton Bovier ... [et al.] 205 $a1st ed. 210 $aAmsterdam ;$aLondon $cElsevier$dc2006 215 $a1 online resource (849 p.) 225 1 $aLes Houches 300 $aDescription based upon print version of record. 311 08$a0-444-52813-X 320 $aIncludes bibliographical references. 327 $aFront 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 327 $aAsymptotics 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 327 $aA 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 Lo?wner evolution; Recent developments; Synopsis; Intersections of random walks; Non-intersection probabilities; Quantum gravity; Random walks on a random lattice 327 $aNon-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 327 $aGeometrical 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 Lo?wner 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 327 $aMultiple paths in O(N), Potts models and SLE 330 $aThe proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians.ˇ introduction to a field of math with many interdisciplinary connections in physics, biology, and computer scienceˇ roadmap to the next decade of mathematical statistical mechanicsˇ volume for reference years to come 410 0$aLes Houches 517 3 $aHouches 2005 session LXXXII 606 $aMathematical physics$vCongresses 606 $aStatistical mechanics$vCongresses 615 0$aMathematical physics 615 0$aStatistical mechanics 676 $a530.15 701 $aBovier$b Anton$f1957-$0300719 712 12$aEcole d'e?te? de physique the?orique (Les Houches, Haute-Savoie, France) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910961433603321 996 $aMathematical statistical physics$94534500 997 $aUNINA