The "second law" of probability.

Please note: this is a joint seminar for mathematics and statistics. <br/> <br/>Abstract: <br/>Most proofs of the central limit theorem give little insight into why we have a right to expect a single distribution whenever we add up small independent quantities. The aim of this talk is to describe the recent solution of a problem going back to Shannon in the 50's, showing that the central limit theorem is driven by an analogue of the the second law of thermodynamics. As we add more random variables and renormalise, the entropy increases and drives the sums toward the Gaussian, which has maximum entropy among all random variables with a given variance. <br/>If $X_i$ are IID square-integrable random variables, then the entropy <br/>\[ Ent \left( \frac{1}{\sqrt{n}} \sum_1^n X_i \right) \] <br/>increases with $n$.