Quasipolynomial-time algorithms for Gibbs point processes

Abstract We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of Gibbs point process interacting via stable potential. This result holds all activities $\lambda$ which satisfies zero-free assumption in neighbourhood interval $[0,\lambda ]$ . As corollary, finiterange potentials, we obtain $\lambda \lt 1/(e^{B + 1} \hat C_\phi )$ where $\hat C_\phi$ is temperedness parameter and $B$ stability constant $\phi$ In special case repulsive potential such as hard-sphere gas improve range activity by factor at least $e^2$ e/\Delta _\phi$ , $\Delta potential-weighted connective Our approximates coefficients cluster expansion uses interpolation method Barvinok to extend this throughout region.