On the spectrum of sum and product of non-hermitian random matrices

By Charles Bordenave. 2010

59 citations recorded by the source corpus.

In this note, we revisit the work of T. Tao and V. Vu on large non-hermitian random matrices with independent and identically distributed (i.i.d.) entries with mean zero and unit variance. We prove under weaker assumptions that the limit spectral distribution of sum and product of non-hermitian random matrices is universal. As a byproduct, we show that the generalized eigenvalues distribution of two independent matrices converges almost surely to the uniform measure on the Riemann sphere.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fef4b665a990dbd006b74531d9071b4c503bf2f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Djalil CHAFAÏ
2. Charles Bordenave
3. Benoît Collins

In Mathematical Physics

1. Charles Bordenave
2. Djalil CHAFAÏ
3. Pietro Caputo
4. Nicholas A. Cook
5. M. Capitaine
6. Van H. Vu
7. Hoi H. Nguyen
8. Terence Tao

In Statistics and Probability

1. Charles Bordenave
2. Djalil CHAFAÏ
3. Nicholas A. Cook
4. Pietro Caputo
5. Terence Tao
6. M. Capitaine
7. Van H. Vu
8. Hoi H. Nguyen

Citations in the corpus

• Around the circular law (2011, background): “We state it here in a slightly stronger form than the original version, see [22].”