Statistical properties of Random Matrices and the replica method

Giorgio Parisi

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arXiv · cond-mat/9701032

Statistical properties of Random Matrices and the replica method

Giorgio Parisi

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Abstract

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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Giorgio Parisi. 1997-01-07. Statistical properties of Random Matrices and the replica method. https://arxiv.org/abs/cond-mat/9701032

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