### On Random Matrices Related to Quantum Informatics

**Pastur, L ***(National Academy of Sciences of Ukraine)*

Monday 17 September 2012, 09:30-10:10

Seminar Room 1, Newton Institute

#### Abstract

We consider two ensembles of random matrices related to certain problems of quantum
informatics. The rst ensemble is a generalization of the Wishart Ensemble viewed as
the sum of independent rank-one operators. However, in contrast to the Wishart
Ensemble the corresponding independent random vectors are the tensor products of
a xed number p 2 of other independent vectors. The second ensemble is also
similar to the Wishart Ensemble viewed as the product of matrix with independent
entries and the transposed (hermitian conjugate) matrix. However, in contrast to the
Wishart Ensemble the corresponding matrix is triangular. We show that the limiting
Normalized Counting Measures can be found from certain functional equations and
discuss their new properties.

#### Presentation

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