Talks

Relative entropy in statistics

We will more carefully examine relative entropy and its properties, and understand its connections to other distance measures between distributions and its role in statistics.

Key concepts: Stein’s lemma, Sanov’s theorem, Pinsker’s inequality, Fidelity.

Entropy and its applications in combinatorics

We will see how standard inequalities about information lead to intuitive proofs of several combinatorial inequalities.

Key concepts: Loomis-Whitney inequality, Bregman’s theorem, Moore bound

Perturbative calculations with light and polynomially self-interacting scalar fields in de Sitter spacetime are commonly plagued by infrared divergences as the scalar fluctuations become strongly coupled on large scales. Using techniques familiar from stochastic inflation, we treat super-Hubble fluctuations non-perturbatively through a probability distribution featuring composite operators of the light scalar. We find that these composite operators behave like late-time conformal primaries and admit a power-law four-point function in position space that is strikingly simple. We attribute physical meaning to these composite operators and conjecture that light interacting scalars in de Sitter in the stochastic picture hadronize into a tower of composite scalars on superhorizon scales. We further investigate whether these composite scalars can be described by a weakly-coupled effective field theory.

Conditional entropy and mutual information

We will consider the problem of transmitting information over a noisy channel, and arrive at Shannon’s channel-coding theorem, in which the notion of mutual information of random variables plays a central role.

Key concepts: Conditional entropy, chain rule for mutual information, capacity of a channel.