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007 | cr nn 008mamaa | ||
008 | 121227s2004 gw | s |||| 0|eng d | ||
020 |
_a9783540399827 _9978-3-540-39982-7 |
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024 | 7 |
_a10.1007/b96719 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBT _2bicssc |
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_aPBT _2thema |
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_aPBWL _2thema |
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082 | 0 | 4 |
_a519.2 _223 |
100 | 1 |
_aTsirelson, Boris. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aVIII, 200 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v1840 |
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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 |
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700 | 1 |
_aPicard, Jean. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b96719 |
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