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1、ZerosofGaussianAnalyticFunctionsandDeterminantalPointProcessesJohnBenHoughManjunathKrishnapurYuvalPeresBálintVirágHBKCAPITALMANAGEMENT350PARKAVE,FL20NEWYORK,NY10022E-mailaddress:jbhough@gmail.comDEPARTMENTOFMATHEMATICS,INDIANINSTITUTEOFSCIENCE,BANGA-LORE560012,KARNATAKA,INDIA.E-mailaddress:manju@
2、math.iisc.ernet.inMICROSOFTRESEARCHONEMICROSOFTWAY,REDMOND,WA98052-6399E-mailaddress:peres@microsoft.comDEPARTMENTOFMATHEMATICSUNIVERSITYOFTORONTO40STGEORGEST.TORONTO,ON,M5S2E4,CANADAE-mailaddress:balint@math.toronto.edu2000MathematicsSubjectClassification.Primary60G55,30B20,30C15,60G15,15A52,60F1
3、0,60D05,30F05,60H25Keywordsandphrases.Gaussiananalyticfunctions,zeros,determinantalprocesses,pointprocesses,allocation,randommatricesContentsPrefaceviiChapter1.Introduction11.1.Randompolynomialsandtheirzeros11.2.Basicnotionsanddefinitions61.3.Hintsandsolutions11Chapter2.GaussianAnalyticFunctions13
4、2.1.ComplexGaussiandistribution132.2.Gaussiananalyticfunctions152.3.Isometry-invariantzerosets182.4.Distributionofzeros-Thefirstintensity232.5.IntensityofzerosdeterminestheGAF292.6.Notes312.7.Hintsandsolutions32Chapter3.JointIntensities353.1.Introduction–Randompolynomials353.2.Exponentialtailofthe
5、numberofzeros373.3.Jointintensitiesforrandomanalyticfunctions393.4.Jointintensities–TheGaussiancase403.5.Fluctuationbehaviourofthezeros42Chapter4.DeterminantalPointProcesses474.1.Motivation474.2.Definitions484.3.Examplesofdeterminantalprocesses534.4.Howtogeneratedeterminantalprocesses634.5.Existen
6、ceandbasicproperties654.6.Centrallimittheorems724.7.Radiallysymmetricprocessesonthecomplexplane724.8.Highpowersofcomplexpolynomialprocesses744.9.Permanentalprocesses754.10.Notes794.11.Hintsandsolutions80Chapter5.TheHyperbolicGAF835.1.Adeterminantalformula835.2.Lawoflargenumbers905.3.Reconstructio
7、nfromthezeroset915.4.Notes95vviCONTENTS5.5.Hintsandsolutions98Chapter6.ADeterminantalZoo996.1.Uniformspanningtrees996.2.Circularunitaryensemble1006.3.Non-normalmatrices,Schurdecompositionandachangeofmeasure1036.4.Ginib
