Quasipolynomial-time algorithms for Gibbs point processes

2022/09/21 by Matthew Jenssen, Jenssen, Matthew, Marcus Michelen +3
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2209.10453

Abstract

We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of a Gibbs point process interacting via a finite-range stable 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, for all finite-range stable potentials we obtain a quasipolynomial-time determinsitic algorithm for all λ< /(e^{B + 1} C_ϕ) where C_ϕ is a temperedness parameter and B is the stability constant of ϕ. In the special case of a repulsive potential such as the hard-sphere gas we improve the range of activity by a factor of at least e² and 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.

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