Statistical properties of Random Matrices and the replica method
Disordered Systems and Neural Networks
2008-02-03 v1 Soft Condensed Matter
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.
Cite
@article{arxiv.cond-mat/9701032,
title = {Statistical properties of Random Matrices and the replica method},
author = {Giorgio Parisi},
journal= {arXiv preprint arXiv:cond-mat/9701032},
year = {2008}
}
Comments
Talk given at Claude Itzykson memorial, June 1996 Paris. 11 pages