#### Room 326

#### Central Limit Theorem: Independent and Free

#### Amritanshu Prasad

##### IMSc

*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.

Done