发表机构
Universitat de Barcelona; Institute of Complex Systems (UBICS), Universitat de Barcelona; Northeastern University（巴塞罗那大学; 复杂系统研究所（UBICS），巴塞罗那大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示泊松撒点因果集在有限区域采样时链接观测量的几何性偏差，提出事件中心乘积窗口估计器以修正偏差，并验证于d=1,2,3维模拟。
AI 中文摘要
泊松撒点提供了一种从连续时空生成因果集的洛伦兹不变方法，但数值工作必然将撒点限制在有限区域内。对于涉及因果集链接的观测量，这种有限体积限制可能产生偏差，且该偏差不会通过简单增加撒点数量而消失。问题的根源在于几何性质。在闵可夫斯基时空中，从某一事件出发，在固定的固有时刻，候选链接分布在非紧致的双曲快度空间中。在维度$d+1$（其中$d\geq 2$）下，该空间是边界主导的：在无限体积极限下，大区域边界附近的体积分数并不趋于零。因此，不同的有限体积正则化可能产生不同的极限归一化统计量。我们将这一现象与非可均空间上朴素开放边界热力学极限的失效联系起来，明确推导了链接固有时分布对有限截断的依赖关系，并区分了定义良好的链接强度轮廓与定义不良的均匀选择链接概念。我们通过独立泊松撒点模拟验证了这些结果，模拟维度为$d+1$，其中$d=1,2,3$。随后，我们提出了一种事件中心乘积窗口估计器，具有受控的双重缩放极限，并讨论了紧致双曲商空间作为无边界替代方案的可能性。
英文摘要
Poisson sprinkling provides a Lorentz-invariant way of generating causal sets from a continuum spacetime, but numerical work necessarily restricts the sprinkling to a finite region. For observables involving causal-set links, this finite-volume restriction can generate a bias that does not disappear by simply increasing the number of sprinkled points. The origin of the problem is geometric. At fixed proper time from an event in Minkowski spacetime, candidate links populate a non-compact hyperbolic space of rapidities. In dimensions $d+1$ with $d\geq 2$, this space is boundary dominated: the fraction of volume close to the boundary of a large region does not vanish in the infinite-volume limit. Different finite-volume regularizations can therefore produce different limiting normalized statistics. We relate this phenomenon to the failure of naive open-boundary thermodynamic limits on non-amenable spaces, derive explicitly the dependence of the link proper-time distribution on the finite cutoff, and distinguish a well-defined link-intensity profile from the ill-defined notion of a uniformly chosen link. We verify these results with independent Poisson-sprinkling simulations in $d+1$ dimensions with $d=1,2,3$. We then propose an event-centered product-window estimator with a controlled double-scaling limit, and discuss compact hyperbolic quotients as a possible boundary-free alternative.
