关于有限随机交错的临界值的精确阶
On the exact orders of critical value in Finitary Random Interlacements
摘要：
本文证明了$\mathbb{Z}^d, \ d\ge 3$中有限无规交错（FRI）的临界强度$u_*(T)$关于期望纤维长度$T$的精确阶数。我们发现，作为$T\to\infty$，$u_*(T)\sim T^{-1}, \ d\ge 5;$ $u_*(T)\sim T^{-1}\log T, \ d=4;$ $u_*(T)\sim T^{-1/2},\ d=3.$我们的估计也给出了数量级的顺序，在该顺序的相对于$T$的相变发生。
英文摘要：
In this paper, we prove the exact orders of critical intensity $u_*(T)$ in Finitary Random Interlacements (FRI) in $\mathbb{Z}^d, \ d\ge 3$ with respect to the expected fiber length $T$. We show that as $T\to\infty$, $u_*(T)\sim T^{-1}, \ d\ge 5;$ $u_*(T)\sim T^{-1}\log T, \ d=4;$ $u_*(T)\sim T^{-1/2},\ d=3.$ Our estimates also give the order of magnitude at which the percolative phase transition with respect to $T$ takes place.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
