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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
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