Lower bounds for contingency tables via Lorentzian polynomials

Abstract

We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok and Gurvits. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes. Our proofs are based on recent results on Lorentzian polynomials.

28 pages

References in corpus (5)

• Exact sampling and counting for fixed-margin matrices
• Efficient Random-Walk Methods for Approximating Polytope Volume
• Bounds on the number of integer points in a polytope via concentration estimates
• Counting Integer Points in Multi-Index Transportation Polytopes
• Phase transition in random contingency tables with non-uniform margins

Cited by in corpus (2)

• Log-concave poset inequalities
• Capacity of Lorentzian polynomials and distance to binomial distributions