5 papers
Spectral Conditions for the Ingleton Inequality
Rostislav Matveev, Andrei Romashchenko
The Ingleton inequality is a classical linear information inequality that holds for representable matroids but fails to be universally valid for entropic vectors. Understanding the…
Beyond Mutual Information: Extension Profiles and Shape Functions of Random Variable Pairs
Rostislav Matveev, Andrei Romashchenko
We study the extension profile of a pair of jointly distributed finite-valued random variables , defined as the set of all triples of numbers …
Structural Properties of Entropic Vectors and Stability of the Ingleton Inequality
Rostislav Matveev, Andrei Romashchenko
We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classic…
Algebraic Barriers to Halving Algorithmic Information Quantities in Correlated Strings
Andrei Romashchenko
We study the possibility of scaling down algorithmic information quantities in tuples of correlated strings. In particular, we address a question raised by Alexander Shen: whether,…
Common information in well-mixing graphs and applications to information-theoretic cryptography
Geoffroy Caillat-Grenier, Andrei Romashchenko, Rustam Zyavgarov
We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph…