探討初抵滲流模型中有關時間常數的嚴格不等式

Abstract

判斷一個有關初抵滲流模型的不等式中等號是否不會成立通常是一個具有挑戰性的問題。在這篇論文中，我們首先討論了由van den Berg和Kesten得出的嚴格不等式，該不等式涉及到兩個不同分佈對應的時間常數。然後，我們將證明對於一個具有特定條件的分佈，不同維度之間的時間常數存在嚴格不等式。

Determining whether an inequality in first-passage percolation can be strict is usually a challenging problem. In this thesis, we first discuss the strict inequality obtained by van den Berg and Kesten, which concerns the time constants corresponding to two different distributions. Then, we will prove that for a fixed distribution with a mild condition, there exists a strict inequality for the time constants between different dimensions.