Adding and multiplying random matrices: a generalization of Voiculescu's formulae
数学物理
2009-10-31 v3 凝聚态物理
高能物理 - 理论
math.MP
摘要
In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulae to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices.
引用
@article{arxiv.math-ph/9810010,
title = {Adding and multiplying random matrices: a generalization of Voiculescu's formulae},
author = {P. Zinn-Justin},
journal= {arXiv preprint arXiv:math-ph/9810010},
year = {2009}
}
备注
11 pages, harvmac. revised x 2: refs and minor comments added