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random matrix theory wigner dyson statistics and beyond lecture notes given at sissa trieste italy v e kravtsov the abdus salam international centre for theoretical physics p o b 586 ...
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...Random matrix theory wigner dyson statistics and beyond lecture notes given at sissa trieste italy v e kravtsov the abdus salam international centre for theoretical physics p o b landau institute kosygina st moscow russia dated today pacs numbers rn m ht i invariant non gaussian ensembles any ensemble rme is determined through probability distribution function pdf that depends on entries an important special class of by nm pdfwhich under rotation basis tmt exp where arbitrary analytic invariance ensured trace tr in front with form eq will be referred to as general corresponds a trivial correlation between uctuating however there one extremely case when hermitean h ii ah this x y n so all uctuate independently around zero celebrated wd note can also generic anm each entry other but variance which indices label simplest rosenzweig porter it remarkable both classic allow exact solution physically describes extended phase randomized states localization eects are negligible contrast account...