LEADER 04524nam 22006735 450 001 996466478103316 005 20201106134243.0 010 $a3-540-39982-8 024 7 $a10.1007/b96719 035 $a(CKB)1000000000231098 035 $a(SSID)ssj0000324378 035 $a(PQKBManifestationID)12071112 035 $a(PQKBTitleCode)TC0000324378 035 $a(PQKBWorkID)10304919 035 $a(PQKB)10980415 035 $a(DE-He213)978-3-540-39982-7 035 $a(MiAaPQ)EBC5591945 035 $a(PPN)155197584 035 $a(EXLCZ)991000000000231098 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Probability Theory and Statistics$b[electronic resource] $eEcole d'Eté de Probabilités de Saint-Flour XXXII - 2002 /$fby Boris Tsirelson, Wendelin Werner ; edited by Jean Picard 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (VIII, 200 p.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1840 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-21316-3 327 $aPreface -- 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. 330 $aThis is yet another indispensable volume for all probabilists and collectors of the Saint-Flour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some two-dimensional random curves. It provides a definition and properties of the Schramm-Loewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1840 606 $aProbabilities 606 $aStatistical physics 606 $aDynamical systems 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 610 1 $aProbability theory 615 0$aProbabilities. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 14$aProbability Theory and Stochastic Processes. 615 24$aComplex Systems. 615 24$aStatistical Physics and Dynamical Systems. 676 $a519.2 686 $a31.70$2bcl 686 $a31.73$2bcl 700 $aTsirelson$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478890 702 $aWerner$b Wendelin$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPicard$b Jean$4edt$4http://id.loc.gov/vocabulary/relators/edt 712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(32nd :$f2002) 906 $aBOOK 912 $a996466478103316 996 $aLectures on Probability Theory and Statistics$92522502 997 $aUNISA