论文标题
强烈的空间混合以进行排斥点过程
Strong spatial mixing for repulsive point processes
论文作者
论文摘要
我们证明，通过有限范围，排斥潜在的$ ϕ $相互作用的Gibbs点过程为活动提供了强大的空间混合属性$λ<e/δ__ϕ $，其中$ Δ_ϕ $是最近在[mp21]中定义的$ ϕ $的潜在接口连接常数。当$λ$满足该结合时，我们会得出几种分析和算法后果：（1）我们证明了这种过程的无限体积压力和表面压力（在表面压力的情况下，存在其存在）。 （2）我们证明了从模型中的本地块动力学，以$ \ Mathbb r^d $ comply in Time $ o（n \ log n）$中的卷中的$ n $（$ n $ n \ log n）$进行采样，从而提供了有效的随机算法来近似分区功能并近似这些模型中的样品。 （3）我们使用上述身份和算法为压力和表面压力提供有效的近似算法。
We prove that a Gibbs point process interacting via a finite-range, repulsive potential $ϕ$ exhibits a strong spatial mixing property for activities $λ< e/Δ_ϕ$, where $Δ_ϕ$ is the potential-weighted connective constant of $ϕ$, defined recently in [MP21]. Using this we derive several analytic and algorithmic consequences when $λ$ satisfies this bound: (1) We prove new identities for the infinite volume pressure and surface pressure of such a process (and in the case of the surface pressure establish its existence). (2) We prove that local block dynamics for sampling from the model on a box of volume $N$ in $\mathbb R^d$ mixes in time $O(N \log N)$, giving efficient randomized algorithms to approximate the partition function and approximately sample from these models. (3) We use the above identities and algorithms to give efficient approximation algorithms for the pressure and surface pressure.
