Quasipolynomial-time algorithms for repulsive Gibbs point processes

09/21/2022

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by   Matthew Jenssen, et al.

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We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of a Gibbs point process interacting via a repulsive potential. This result holds for all activities λ for which the partition function satisfies a zero-free assumption in a neighborhood of the interval [0,λ]. As a corollary, we obtain a quasipolynomial-time deterministic approximation algorithm for all λ < e/Δ_ϕ, where Δ_ϕ is the potential-weighted connective constant of the potential ϕ. Our algorithm approximates coefficients of the cluster expansion of the partition function and uses the interpolation method of Barvinok to extend this approximation throughout the zero-free region.