Partial traces and entropy inequalities

Partial Commutation and Traces

Hypergraphs, Entropy, and Inequalities

1. INTRODUCTION. Hypergraphs. Information Theory. Cauchy-Schwarz. It seems reasonable to assume that most mathematicians would be puzzled to find these three terms as, say, key words for the same mathematical paper. (Just in case this puzzlement is a result of being unfamiliar with the term " hypergraph " : a hypergraph is nothing other than a family of sets, and will be defined formally later....

Representation of Partial Traces

The notion of trace in a monoidal category has been introduced to give a categorical account of a situation occurring in very different settings: linear algebra, topology, knot theory, proof theory. . . with the trace operation understood as a feedback operation. Partially traced categories were later introduced to account for cases where the trace is not always defined, and it was shown that p...

Diffusion equations and entropy inequalities

The present notes contain the material presented at the XLI Summer School on Mathematical Physics (Ravello September 05 10, 2016). The notes aim in introducing a physical way to look at well-known functional inequalities in sharp form. Among them, the classical Young’s inequality and its converse in sharp form, BrascampLieb type inequalities, Babenko’s inequality and Prékopa-Leindler inequality...

Moment - Entropy Inequalities