论文标题
欧几里得第一阶段渗透的非随机波动的差异
Divergence of non-random fluctuation for Euclidean first-passage percolation
论文作者
论文摘要
非随机波动是第一次通道渗透中的中心对象之一。它在[sutha nakajima中得到了证明。第一次通过渗透中非随机波动的差异。 {\ em电子。社区。 Prob。} 24（65），1-13。 [2019年]，对于特定的渐近方向，它在晶格的第一通道渗透中分歧，并具有明确的下限。在本文中，我们讨论了Euclidean首次通行渗透中的非随机波动，并表明它在该模型中也以尺寸差异$ d \ geq 2 $。与\ cite {n19}的结果相比，目前的结果被证明了任何方向并改善了下限。
The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {\em Electron. Commun. Probab.} 24 (65), 1-13. 2019.] that for a particular asymptotic direction, it diverges in a lattice first passage percolation with an explicit lower bound. In this paper, we discuss the non-random fluctuation in Euclidean first passage percolations and show that it diverges in dimension $d\geq 2$ in this model also. Compared with the result in \cite{N19}, the present result is proved for any direction and improves the lower bound.
