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arXiv · 2111.04809

Absence of zeros implies strong spatial mixing

Guus Regts
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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.

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Guus Regts. 2021-11-08. Absence of zeros implies strong spatial mixing. https://doi.org/10.1007/s00440-023-01190-z

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