Thisbookgivesacoherentanddetaileddescriptionofanalyticalmethodsdevisedtostudyrandommatrices.Thesemethodsarecriticaltotheunderstandingofvariousfieldsininmathematicsandmathematicalphysics,suchasnuclearexcitations,ultrasonicresonancesofstructuralmaterials,chaoticsystems,thezerosoftheRiemannandotherzetafunctions.Moregenerallytheyapplytothecharacteristicenergiesofanysufficientlycomplicatedsystemandwhichhavefound,sincethepublicationofthesecondedition,manynewapplicationsinactiveresearchareassuchasquantumgravity,trafficandcommunicationsnetworksorstockmovementinthefinancialmarkets.Thisrevisedandenlargedthirdeditionreflectsthelatestdevelopementsinthefieldandconveyagreaterexperiencewithresultspreviouslyformulated.Forexample,thetheoryofskew-orthogoanlandbi-orthogonalpolynomials,paralleltothatofthewidelyknownandusedorthogonalpolynomials,isexplainedhereforthefirsttime.
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随机矩阵理论