Jennifer Pi

From Classical Entropy to Free Entropy

There are two main notions of entropy from probability theory, which coincide in the classical setting. These two constructions led Voiculescu to define different notions of entropy in the setting of free probability, called microstates and non-microstates free entropy. In this talk, I'll discuss the classical setting as motivation, then move to the free setting. In joint work with David Jekel, we relate each notion of free entropy back to an appropriate limit of classical entropic quantities, which proves an inequality between the two notions of free entropy.