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001 978-3-540-39982-7
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005 20190213151814.0
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008 121227s2004 gw | s |||| 0|eng d
020 _a9783540399827
_9978-3-540-39982-7
024 7 _a10.1007/b96719
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aTsirelson, Boris.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLectures on Probability Theory and Statistics
_h[electronic resource] :
_bEcole d'Eté de Probabilités de Saint-Flour XXXII - 2002 /
_cby Boris Tsirelson, Wendelin Werner ; edited by Jean Picard.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2004.
300 _aVIII, 200 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1840
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aStatistical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
700 1 _aWerner, Wendelin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aPicard, Jean.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540213161
776 0 8 _iPrinted edition:
_z9783662163535
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1840
856 4 0 _uhttps://doi.org/10.1007/b96719
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11944
_d11944