资源描述：
《2012_user-friendly tail bounds for sums of random matrices_FOCM》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、FoundComputMath(2012)12:389434DOI10.1007/s10208-011-9099-zUser-FriendlyTailBoundsforSumsofRandomMatricesJoelA.TroppReceived:16January2011/Accepted:13June2011/Publishedonline:2August2011©TheAuthor(s)2011.ThisarticleispublishedwithopenaccessatSpringerlink.comAbstractThispaperpresentsnewprobab
2、ilityinequalitiesforsumsofindependent,random,self-adjointmatrices.Theseresultsplacesimpleandeasilyverifiablehy-pothesesonthesummands,andtheydeliverstrongconclusionsaboutthelarge-deviationbehaviorofthemaximumeigenvalueofthesum.Tailboundsforthenormofasumofrandomrectangularmatricesfollowasanimm
3、ediatecorollary.Theprooftechniquesalsoyieldsomeinformationaboutmatrix-valuedmartingales.Inotherwords,thispaperprovidesnoncommutativegeneralizationsoftheclassi-calboundsassociatedwiththenamesAzuma,Bennett,Bernstein,Chernoff,Hoeffd-ing,andMcDiarmid.Thematrixinequalitiespromisethesamediversity
4、ofapplica-tion,easeofuse,andstrengthofconclusionthathavemadethescalarinequalitiessovaluable.KeywordsDiscrete-timemartingale·Largedeviation·Probabilityinequality·Randommatrix·SumofindependentrandomvariablesMathematicsSubjectClassification(2000)Primary60B20·Secondary60F10·60G50·60G42Communicat
5、edbyAlbertCohen.J.A.Tropp()Computing&MathematicalSciences,MC305-16,CaliforniaInstituteofTechnology,Pasadena,CA91125,USAe-mail:jtropp@cms.caltech.edu390FoundComputMath(2012)12:3894341IntroductionRandommatriceshavecometoplayasignificantroleincomputationalmathemat-ics.Thislineofresearchhasadva
6、ncedbyusingestablishedmethodsfromrandommatrixtheory,butithasalsogenerateddifficultquestionsthatcannotbeaddressedwithoutnewtools.Letussummarizesomeofthechallengesthatariseinnumericalapplications.•Researchhasextendedwellbeyondtheclassicalensembles(e.g.,WishartmatricesandWignermatrices)toencomp
7、assmanyotherclassesofrandommatrices.Forinstance,itisnowcommontostudythepropertiesofasparsematrixsampledfromafixedmatrixorarandomsubmatrixdrawnfromafixedmatrix.•Wealsoencounterhighlystructuredmatricesthatinvolvealimitedamountofran-domness.Oneimportantexampl
