A replica approach to products of random matrices
Disordered Systems and Neural Networks
2009-10-30 v1
Abstract
We analyse products of random matrices by means of a variant of the replica trick which was recently introduced for one-dimensional disordered Ising models. The replicated transfer matrix can be block-diagonalized with help of irreducible representations of the permutation group. We show that the free energy (or the Lyapunov exponent) of the product corresponds to the replica symmetric representation, whereas non-trivial representations correspond to certain correlation functions.
Keywords
Cite
@article{arxiv.cond-mat/9709009,
title = {A replica approach to products of random matrices},
author = {M. Weigt},
journal= {arXiv preprint arXiv:cond-mat/9709009},
year = {2009}
}
Comments
12 pages, REVTeX, 2 eps figures, submitted to J. Phys. A: Math. Gen