On the Asymptotic Spectrum of Products of Independent Random Matrices.

We consider products of independent random matrices with independent entries. The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let X (�)

[1]  On the asymptotic distribution of singular values of products of large rectangular random matrices , 2010, 1012.2586.

[2]  F. Götze,et al.  Asymptotic distribution of singular values of powers of random matrices , 2010, 1002.4442.

[3]  R. Speicher,et al.  Sharp bounds for sums associated to graphs of matrices , 2009, 0909.4277.

[4]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[5]  Teodor Banica,et al.  Free Bessel Laws , 2007, Canadian Journal of Mathematics.

[6]  Chien-Hwa Hwang,et al.  Asymptotic Theorems for the Product of Certain Structured Random Matrices and Their Application to Analysis of Asynchronous CDMA , 2009, IEEE Transactions on Information Theory.

[7]  J. H. van Lint,et al.  Functions of one complex variable II , 1997 .

[8]  On the singular spectrum of powers and products of random matrices , 2010 .

[9]  J. Conway Functions of One Complex Variable II , 1978 .

[10]  Z. Burda,et al.  Spectrum of the product of independent random Gaussian matrices. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Zhidong Bai,et al.  On limit theorem for the eigenvalues of product of two random matrices , 2007 .

[12]  Z. D. Bai,et al.  Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang , 1986 .

[13]  Uffe Haagerup,et al.  A new application of random matrices: Ext(C^*_{red}(F_2)) is not a group , 2002 .

[14]  Terence Tao,et al.  Random matrices: Universality of ESDs and the circular law , 2008, 0807.4898.

[15]  E. Saff,et al.  Logarithmic Potentials with External Fields , 1997, Grundlehren der mathematischen Wissenschaften.

[16]  B. Maurey Some deviation inequalities , 1990, math/9201216.

[17]  Alexander Tikhomirov,et al.  The circular law for random matrices , 2007, 0709.3995.