Statistical properties of Random Matrices and the replica method

Details Statistical properties of Random Matrices and the replica method Statistical properties of Random Matrices and the replica method

1997-01-07

arxiv.org/abs/cond-mat/9701032v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Talk given at Claude Itzykson memorial, June 1996 Paris. 11 pages

Scientific paper

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the limits of validity of this expansion are carefully analyzed. A comparison is done with a similar model with quenched disorder, where the solution can be found by using the replica method. Finally I will apply these results to a model which should describe the liquid-glass transitionin high dimensions.

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