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100   $a20160711j20160731  fy             0
101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aFree Probability and Operator Algebras$b[electronic resource] /$fDan-Virgil Voiculescu, Nicolai Stammeier, Moritz Weber
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016
215   $a1 online resource (142 pages)
225 0 $aMu?nster Lectures in Mathematics (MLM) ;$x2523-5230
311   $a3-03719-165-1 
327   $tBackground and outlook /$rDan-Virgil Voiculescu --$tBasics in free probability /$rMoritz Weber --$tRandom matrices and combinatorics /$rRoland Speicher --$tFree monotone transport /$rDimitri L. Shlyakhtenko --$tFree group factors /$rKen Dykema --$tFree convolution /$rHari Bercovici --$tEasy quantum groups /$rMoritz Weber.
330   $aFree probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices etc). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescu's attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication.  These lecture notes arose from a masterclass in Mu?nster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). In order to make it more accessible, the exposition features a chapter on basics in free probability, and exercises for each part.  This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras.
606   $aFunctional analysis$2bicssc
606   $aGroups & group theory$2bicssc
606   $aFunctional analysis$2msc
606   $aGroup theory and generalizations$2msc
606   $aOperator theory$2msc
606   $aProbability theory and stochastic processes$2msc
615 07$aFunctional analysis
615 07$aGroups & group theory
615 07$aFunctional analysis
615 07$aGroup theory and generalizations
615 07$aOperator theory
615 07$aProbability theory and stochastic processes
686   $a46-xx$a20-xx$a47-xx$a60-xx$2msc
701   $aVoiculescu$b D. V$g(Dan V.),$f1949-$048579
701   $aStammeier$b Nicolai$01070783
701   $aWeber$b Moritz$01070784
801  0$bch0018173
906   $aBOOK
912   $a9910153279703321
996   $aFree Probability and Operator Algebras$92565054
997   $aUNINA