Arrow Contraction and Expansion in Tropical Diagrams

Abstract

Arrow contraction applied to a tropical diagram of probability spaces is a modification of the diagram, replacing one of the morphisms with an isomorphism while preserving other parts of the diagram. It is related to the rate regions introduced by Ahlswede and Körner. In a companion article, we use arrow contraction to derive information about the shape of the entropic cone. Arrow expansion is the inverse operation to the arrow contraction.

Keywords

• tropical probability
• entropic cone