标题： 原初黑洞在跃迁集理论中的聚集 显示英文标题

标题： Clustering of Primordial Black Holes in Excursion Set Theory

摘要： 我们研究了原初黑洞（PBHs）在运动轨迹理论（EST）框架内的聚类情况。 EST形式化方法被扩展，以计算在聚类距离内形成PBH对的联合概率，基于具有共同历史的两条随机轨迹。 我们的结果表明，增强的功率谱不仅增加了特定质量范围内的PBH形成，还增强了它们的聚类概率。 我们发现蓝倾斜的光谱指数与PBH形成和聚类的质量范围之间存在一一对应关系。 此外，我们证明了聚类概率随着聚类距离的增加而渐近减少，而较高的临界密度阈值（障碍）会导致聚类丰富度的抑制。 显示英文摘要

摘要： We investigate the clustering of Primordial Black Holes (PBHs) within the framework of Excursion Set Theory (EST). The EST formalism is extended to compute the joint probability of forming PBH pairs within a clustering distance, based on two stochastic trajectories with a shared history. Our results show that an enhanced power spectrum not only increases the formation of PBHs in specific mass ranges but also enhances their clustering probability. We find a one-to-one correspondence between the blue-tilted spectral index and the mass ranges in which PBHs form and cluster. Additionally, we demonstrate that the clustering probability decreases asymptotically with increasing clustering distance, while a higher critical density threshold (barrier) leads to a suppression of clustering abundance.