d>4时，$\boldsymbol{\rm Z}^d$上的泊松动物园（Poisson Zoos）与环汤渗流，以及d≥3时$\boldsymbol{\rm T}_d$上的临界参数的（非）重合性
(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on $\mathbb{Z^d}$, $d > 4$, and $\mathbb{T}_d$,$ d \ge 3$
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中文总结 AI 辅助
本研究针对d>4的Z^d及d≥3的T_d，探讨泊松动物园与环汤渗流的临界参数（非）重合性，证明d≥5时Z^d上离散图与对应度量图的环汤渗流临界参数存在差异，还推导了树上泊松动物园渗流与磁化率的临界参数重合结论，并发展了长程相关渗流对伯努利增强的敏感性概念。
中文摘要 AI 辅助
本文研究各类相关渗流问题的临界参数的（非）重合性。更准确地说，对于随机游走环汤（random walk loop soup），我们证明在d≥5的$\boldsymbol{\rm Z}^d$上，离散图与对应度量图的渗流问题临界参数存在差异；此外，在树上，我们推导得出类似结论，同时针对更广泛的渗流问题类别——即所谓的泊松动物园（Poisson zoo），得出渗流与磁化率的临界参数重合的结论。在此过程中，我们基于先前提出的增强思路，发展出对这类具有长程相关性的渗流问题的伯努利增强的敏感性这一有用概念。
英文摘要
In this article we investigate the (non)-coincidence of critical parameters for various related percolation problems. More precisely, for the random walk loop soup we show that on $\mathbb Z^d$, $d\ge 5$, the critical parameters for the percolation problems differ on the discrete graph and the respective metric graph. Moreover, on trees we deduce an analogous statement as well as the coincidence of the critical parameters for percolation and susceptibility for a more general class of percolation problems, the so-called Poisson zoo. Along the way we develop the useful notion of sensitivity to Bernoulli enhancements of such percolation problems with long range correlations, which builds on previously developed enhancement ideas.
