Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices

Autor:	Burda, Z., Jarosz, A., Livan, G., Nowak, M. A., Swiech, A.
Rok vydání:	2010
Předmět:	Condensed Matter - Statistical Mechanics Mathematical Physics
Zdroj:	Phys. Rev. E 82, 061114 (2010)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.82.061114
Popis:	We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that they both have power-law behavior at zero and determine the corresponding powers. We also propose a heuristic form of finite size corrections to these expressions which very well approximates the distributions for matrices of finite dimensions. Comment: 13 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1007.3594 Zobrazit plný text záznamu View this record from Arxiv