The Free Central Limit Theorem is a fundamental result in the theory of free probability that describes the behavior of sums of non-commuting random variables. It states that under certain conditions, the distribution of the normalized sum of free random variables converges to a free version of the normal distribution. This theorem is closely related to concepts like free cumulants, providing a framework for understanding how large collections of free random variables behave, and has significant implications in understanding free Brownian motion and the structure of free products of von Neumann algebras.
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