Student Probability Seminar

A Look at CLTs in Banach Spaces

Speaker: Douglas Dow, CIMS

Location: Warren Weaver Hall 312

Date: Tuesday, April 19, 2022, 9:50 a.m.

Synopsis:

Probably one of the most used theorems in probability, the Central Limit Theorem states that the sum of n i.i.d. copies of a random variable behaves like a Gaussian for large n. Writing down the statement of the CLT requires at least a measurable vector space structure, so one might wonder if the CLT holds in much greater generality, for instance for Banach valued random variables. I will lay out some of the main nuances and difficulties to Banach space probability and then present a result proving a CLT in certain Lp spaces. If time permits we will discuss an application to a central limit theorem for empirical measures on $\mathbb{R}$ .