ﻻ يوجد ملخص باللغة العربية
We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of the matrices, are operator valued semicircular laws. Furthermore, we prove an operator valued analogue of Voiculescus asymptotic freeness theorem. By replacing conditional independence with Boolean independence, we show that the limit laws of the random matrices are Operator-valued Bernoulli laws.
We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives a example where the partial transpose pro
We adapt the theory of chordal Loewner chains to the operator-valued matricial upper-half plane over a $C^*$-algebra $mathcal{A}$. We define an $mathcal{A}$-valued chordal Loewner chain as a subordination chain of analytic self-maps of the $mathcal{A
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can easily study t
In this paper two independent and unitarily invariant projection matrices P(N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomials of them as the matrix size $N$ converges to infinity. The result is
We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and Thorbjornsen where GU