I will present a brief overview of 1-bounded entropy, which is a modification of Voiculescu's free entropy dimension for tuples, and is known to be an invariant of the generated von Neumann algebra. After briefly discussing the definition, I will focus on its relation to the Peterson-Thom conjecture. Particularly, how it can be used to reduce this conjecture to a problem on strong convergence in random matrices (a problem that several different sets of authors have recently claimed solutions to).
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