From: Marvin the Robot Subject: Re: COMPREHENSIVE References Sought for Random Matrices in Number Theory Date: Wed, 16 Aug 2000 16:53:51 -0500 Newsgroups: sci.math Summary: [missing] David Pollen wrote: > FULL SUBJECT: References sought for: Random Matrices and Markoff > Processes in Number Theory and Harmonic Differential Forms of Specifically > Curved Infinite Dimensional Algebraic Varieties That's quite a mouthful. It sounds like you are trying to prove the Riemann hypothesis. > Can people post me some COMPLETELY COMPREHENSIVE advanced > references to > learning statistics and random matrix theory for number theory. Mehta's book is the standard ref for random matrices. Sarnak/Katz book on level spacing and Frobenius eigenvalues. Numerous papers in the LANL math and physics archives (xxx.lanl.gov) on "universality" of various probability distributions. > I have > some exciting new ideas for a long while about the subject on a way such > matrices could be automatically forced to have certain highly non-obvious > structural constraints well, well beyond the usual silly > elementary eigenvalue distribution stuff. Preserving a quadratic form and probabilistic or positivity properties are all known to do what I suspect you're after. Anyway, see e.g. Burnol's articles at the LANL archive. > But I don't want to miss anything in the literature since I'm > self-taught in this area in the last six years and don't have anybody > to talk to that is a statistics expert. > So I appeal to that statistics and random matrix experts for references. > Also I am seeking any references to any papers that might hint or > examine deep implications that such matrices and Markoff processes might > highly and subtly restrict the potential cohomology values > that algebraic geometry varieties can have Deninger papers on infinite-dimensional approach to RH, in Motives conference proceedings and elsewhere. > viewed > from a hodge theoretic differential geometric viewpoint of > harmonic forms (of course) with certain differential geometry > curvature constraints being the only conditions on these infinite > dimensional and sometimes even Abelian varieties. Lempert's papers at xxx.lanl.gov. > My ideas would > be ultimately that this would happen "for free" automatically as > a non-trivial result of some complicated new statistical ideas I have. > (I can't find any references to the specific kind of stuff I've > been thinking If you tell the specific stuff you've been thinking you'll get better advice. > and can't imagine anybody else would have > thought of it of but maybe I have > been unlucky I've come up totally empty so far even though I have totally > poured through > this stuff for like weeks full time in the library.) So maybe if > this works it would be new!!!! Posting it to the net or LANL would establish priority and elicit feedback.