Abstract
AbstractIn this paper we show that absence of complex zeros of the partition function of the hard-core model on any family of bounded degree graphs that is closed under taking induced subgraphs implies that the associated probability measure, the hard-core measure, satisfies strong spatial mixing on that family. As a corollary we obtain that the hard-core measure on the family of bounded degree claw-free graphs satisfies strong spatial mixing for every value of the fugacity parameter. We furthermore derive strong spatial mixing for graph homomorphism measures from absence of zeros of the graph homomorphism partition function.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
Reference41 articles.
1. Alimohammadi, Y., Anari, N., Shiragur, K., Vuong, T.D.: Fractionally log-concave and sector-stable polynomials: counting planar matchings and more. In: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 433–446 (2021)
2. Bandyopadhyay, A., Gamarnik, D.: Counting without sampling. New algorithms for enumeration problems using statistical physics. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 890–899. ACM, New York (2006)
3. Algorithms and Combinatorics;A Barvinok,2016
4. Barvinok, A.: Approximating real-rooted and stable polynomials, with combinatorial applications. Online J. Anal. Comb. 14, 13 (2019)
5. Barvinok, A., Soberón, P.: Computing the partition function for graph homomorphisms. Combinatorica 37(4), 633–650 (2017)