Curvature of basis exchange walks

2025/09/23 by Isabel Detherage, Detherage, Isabel
Biochemistry, Genetics and Molecular Biology · Medicine · Pharmacology, Toxicology and Pharmaceutics · #05B35 #49Q22 #60J10 #Chemical Reactions and Isotopes #Combinatorics (math.CO) #DNA and Nucleic Acid Chemistry #FOS: Mathematics #Monoclonal and Polyclonal Antibodies Research #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2509.18510

openalex publication_date 2025/09/23 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We prove both lower and upper bounds on the Ollivier-Ricci curvature of the basis exchange walk on a matroid. We give several examples of non-negatively curved basis exchange walks and negatively curved basis exchange walks.

Citations

• From Coupling to Spectral Independence and Blackbox Comparison with the Down-Up Walk
• On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization
• Modified log-Sobolev inequalities for strongly log-concave distributions
• Log-Concave Polynomials I: Entropy and a Deterministic Approximation Algorithm for Counting Bases of Matroids
• Ricci curvature of Markov chains on metric spaces
• Ricci curvature of Markov chains on metric spaces

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