Asymptotic Infinitesimal Freeness with Amalgamation for Haar Quantum Unitary Random Matrices

作者：Curran Stephen^*; Speicher Roland

来源：Communications in Mathematical Physics, 2011, 301(3): 627-659.

DOI：10.1007/s00220-010-1164-y

We consider the limiting distribution of U(N)A(N)U(N)* and B(N) (and more general expressions), where A(N) and B(N) are N x N matrices with entries in a unital C*-algebra B which have limiting B-valued distributions as N -> infinity, and U(N) is a N x N Haar distributed quantum unitary random matrix with entries independent from B. Under a boundedness assumption, we show that U(N)A(N)U(N)* and B(N) are asymptotically free with amalgamation over B. Moreover, this also holds in the stronger infinitesimal sense of Belinschi-Shlyakhtenko.
We provide an example which demonstrates that this result may fail for classical Haar unitary random matrices when the algebra B is infinite-dimensional.

• 出版日期2011-2