The Free Central Limit Theorem is a fundamental result in noncommutative probability that describes the behavior of sums of independent random variables in a noncommutative setting. It generalizes the classical central limit theorem by showing that under certain conditions, the distribution of normalized sums of free random variables converges to a free Gaussian distribution as the number of variables increases. This theorem is crucial for understanding the connection between free probability and classical probability, especially in the context of operator algebras.
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