Wednesday, June 21 2023
14:00 - 15:00

Room 326

Central Limit Theorem: Independent and Free

Amritanshu Prasad


The central limit theorem for independent identically distributed random variables with all moments finite has a simple proof using the method of moments. A similar proof works for free identically distributed non-commutative random variables.

In the independent case, the limiting distribution is the Gaussian, with nth moment given by perfect matchings of n elements. In the latter case, only non-crossing matchings occur.

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