论文标题
Gibbs点过程
Quasipolynomial-time algorithms for Gibbs point processes
论文作者
论文摘要
我们证明了通过有限范围稳定势相互作用的Gibbs点过程的分区函数的准化性时间确定性近似算法。该结果适用于所有活动$λ$，分区函数在间隔$ [0，λ] $的附近满足无零假设。作为推论，对于所有有限范围的稳定电势，我们获得了所有$λ< /（e^{b + 1} \ hat c_Dcartions $ c_ent $ \ hat c_Dcartion $ compants $均为$ b $的稳定性常量为$ $ nistability $ $。在具有排斥潜力的特殊情况下，例如硬球气体，我们将活动范围提高至少$ e^2 $，并获得所有$λ<e/δ__$的quasipolyNomial-exipition确定性近似算法，其中$Δ_x$是潜在的电位连接常数。我们的算法近似分区函数的群集扩展的系数，并使用Barvinok的插值方法扩展了整个无零区域的近似值。
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 $λ< /(e^{B + 1} \hat C_ϕ)$ where $\hat C_ϕ$ 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 $e^2$ 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.
