Some intuitive proofs of central limit theorems

We will study some “intuitive” proofs of central limit theorems, based on ideas by Stein (1972). (The “unintuitive” proofs of the central limit theorems are the ones using characteristic functions and Fourrier analysis).

• Stein, C. (1972). “A bound for the error in the normal approximation to the distribution of a sum of dependent random variables”. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2. University of California Press. pp. 583–602. MR 0402873.
• The book “A User’s Guide to Measure Theoretic Probability” by David Pollard.

Presenter: Pierre Bellec