Absence of zeros implies strong spatial mixing
arXiv:2111.04809 · doi:10.1007/s00440-023-01190-z
Abstract
In 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 implies that the associated probability measure, the \emph{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. We furthermore derive strong spatial mixing for graph homomorphism measures from absence of zeros of the graph homomorphism partition function.
v4 some small changes based on comments by referees