|Apr 06, 2022
Free probability theory is a non-commutative analogue of classical probability theory where ``freeness'' replaces ``independence'', introduced by Voiculescu along his study of free group factors. Free probability connects random matrices to free group factors, in the sense that independent, large-dimensional random matrices can serve as generators of free group factors. Conversely, free probability has been used as a crucial tool in studies of random multi-matrix models. In this talk, we first recall how free probability theory is formulated and connected to random matrices, and then we will look at some of the instances where operator algebra and random matrix theory shed light to one another.
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