03173nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202245012400238260008200362300003400444336002600478337002600504338003600530347002400566490005600590505032800646506006600974520128401040650003202324650003402356650002902390650004202419650002502461650005302486700003702539700003302576700002802609856003202637856007002669208-160711CH-001817-320160711234501.0a fot ||| 0|cr nn mmmmamaa160711e20160731sz fot ||| 0|eng d a978303719665670a10.4171/1652doi ach0018173 7aPBKG2bicssc 7aPBFD2bicssc a46-xxa20-xxa47-xxa60-xx2msc10aFree Probability and Operator Algebrash[electronic resource] /cDan-Virgil Voiculescu, Nicolai Stammeier, Moritz Weber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (142 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aMünster Lectures in Mathematics (MLM) ;x2523-523000tBackground 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.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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 Münster, 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.07aFunctional analysis2bicssc07aGroups & group theory2bicssc07aFunctional analysis2msc07aGroup theory and generalizations2msc07aOperator theory2msc07aProbability theory and stochastic processes2msc1 aVoiculescu, Dan-Virgil,eeditor.1 aStammeier, Nicolai,eeditor.1 aWeber, Moritz,eeditor.40uhttps://doi.org/10.4171/165423cover imageuhttps://www.ems-ph.org/img/books/voiculescu_mini.jpg