000 | 04111nam a22005535i 4500 | ||
---|---|---|---|
001 | 978-3-540-69897-5 | ||
003 | DE-He213 | ||
005 | 20190213151142.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2009 gw | s |||| 0|eng d | ||
020 |
_a9783540698975 _9978-3-540-69897-5 |
||
024 | 7 |
_a10.1007/978-3-540-69897-5 _2doi |
|
050 | 4 | _aQA150-272 | |
072 | 7 |
_aPBD _2bicssc |
|
072 | 7 |
_aMAT008000 _2bisacsh |
|
072 | 7 |
_aPBD _2thema |
|
082 | 0 | 4 |
_a511.1 _223 |
100 | 1 |
_aGuionnet, Alice. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aLarge Random Matrices: Lectures on Macroscopic Asymptotics _h[electronic resource] : _bÉcole d'Été de Probabilités de Saint-Flour XXXVI ¿ 2006 / _cby Alice Guionnet. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2009. |
|
300 |
_aXII, 294 p. 13 illus. _bonline resource. |
||
336 |
_atext _btxt _2rdacontent |
||
337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
||
347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v1957 |
|
505 | 0 | _aWigner matrices and moments estimates -- Wigner#x2019;s theorem -- Wigner's matrices; more moments estimates -- Words in several independent Wigner matrices -- Wigner matrices and concentration inequalities -- Concentration inequalities and logarithmic Sobolev inequalities -- Generalizations -- Concentration inequalities for random matrices -- Matrix models -- Maps and Gaussian calculus -- First-order expansion -- Second-order expansion for the free energy -- Eigenvalues of Gaussian Wigner matrices and large deviations -- Large deviations for the law of the spectral measure of Gaussian Wigner's matrices -- Large Deviations of the Maximum Eigenvalue -- Stochastic calculus -- Stochastic analysis for random matrices -- Large deviation principle for the law of the spectral measure of shifted Wigner matrices -- Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials -- Asymptotics of some matrix integrals -- Free probability -- Free probability setting -- Freeness -- Free entropy -- Basics of matrices -- Basics of probability theory. | |
520 | _aRandom matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen. | ||
650 | 0 | _aDistribution (Probability theory. | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aMatrix theory. | |
650 | 0 | _aFunctional analysis. | |
650 | 0 | _aCombinatorics. | |
650 | 1 | 4 |
_aDiscrete Mathematics. _0http://scigraph.springernature.com/things/product-market-codes/M29000 |
650 | 2 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
650 | 2 | 4 |
_aAlgebra. _0http://scigraph.springernature.com/things/product-market-codes/M11000 |
650 | 2 | 4 |
_aLinear and Multilinear Algebras, Matrix Theory. _0http://scigraph.springernature.com/things/product-market-codes/M11094 |
650 | 2 | 4 |
_aFunctional Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12066 |
650 | 2 | 4 |
_aCombinatorics. _0http://scigraph.springernature.com/things/product-market-codes/M29010 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540866107 |
776 | 0 | 8 |
_iPrinted edition: _z9783540698968 |
830 | 0 |
_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v1957 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-540-69897-5 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c9701 _d9701 |