On some optimization problems involving matrices of large sizes

In this talk, we study the Biane and Voiculescu metric and state a duality result. We comment on limits of systems of d-tuples of n x n matrices, as n tend to infinity. Our study was motivated by the desired of finding appropriate metrics for equations in quantum mechanics, but may also be relevant in quantum game theory. (This talk is based on a joint work with D. Jekel, K. Nam and D. Shlyakhtenko).

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