Collection Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Organizer(s)
Date(s)
13/05/2024
Geometry of the entropy region
A three-lecture series covering some recent research on the geometry of the entropy region. The lectures will cover: 1) Shannon inequalities; the case of one, two and three variables. Reducing dimensions. 2) The closure of the entropy region is a closed convex cone. 3) Defining distributions: partition, vector, group based distributions. The “ringing bell” distribution. 4) Finding new entropy inequalities, the methods of Zhang-Yeung, Makcharychev, Matus, Maximum entropy method. Using ITIP to check Shannon inequalities. 5) Private information, dimension reduction, symmetrization. 6) The case of four random variables. Ingleton coordinate; structure of Γ_4. Generating new inequalities. 7) Γ_4 is not polyhedral – Matus’ proof 8) Systematic search for new inequalities: methods, algorithms, results.
