Disordered random matrices

4th International Workshop on Statistical Physics and Mathematics for Complex Systems

物理学;数学

Pato, M.P.^1

Instítuto de Física, Universidade de São Paulo, Caixa Postal 66318, São Paulo, S.P.

05314-970, Brazil^1

关键词: Adjacency matrices;    Positive random variables;    Random graphs;    Random matrices;    Random matrix theory;    Scale-free model;    Statistical properties;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/604/1/012015/pdf
DOI  :  10.1088/1742-6596/604/1/012015

来源: IOP

【 摘 要 】

A revision is made of the effect, in the statistical properties of the matrices of random matrix theory, of dividing them by a positive random variable. As the method preserves unitary invariance analitical derivations are easily performed. It is shown that the same procedure applied to the adjacency matrices of random graphs gives rise to a family of graphs that interpolates between the Erdos-Renyiand the scale-free model. Previous applications and new ones are discussed.