标题： 一阶通过渗透中标度指数之间的关系的简化证明 显示英文标题

标题： A simplified proof of the relation between scaling exponents in first-passage percolation

摘要： 在最近的突破性工作中，Chatterjee [Ann. of Math. (2) 177 (2013) 663-697]证明了一个长期存在的猜想，该猜想将第一 passage percolation 在$\mathbb{Z}^d$上的横向指数$\xi$和波动指数$\chi$联系起来。本文的目的是替换 Chatterjee (2013) 的主要论证，并给出这个关系的另一种证明。具体来说，我们证明了在假设 Chatterjee (2013) 中定义的指数存在的情况下，有关系$\chi\leq2\xi-1$。我们论证的一个优势是它不需要 Chatterjee (2013) 的“近 Gamma”假设。 显示英文摘要

摘要： In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent $\xi$ and the fluctuation exponent $\chi$ in first-passage percolation on $\mathbb{Z}^d$. The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation $\chi\leq2\xi-1$. One advantage of our argument is that it does not require the "nearly Gamma" assumption of Chatterjee (2013).