Rostislav Matveev — Tropical Probability and Entropic Inequalities

Tropical Probability is a new method to address problems in Information Theory and related fields of research, that is being developed in collaboration with J. Portegies (TU/e). We consider the monoid of commutative diagrams of probability spaces and look at its asymptotic cone. The dual cone roughly correspond to the space of bounded characters on the original monoid. Its elements are entropy-like quantities.

I will briefly explain our ideas and present one of the applications of the theory outside of itself, more specifically, to the entropic (non-Shannon) inequalities.