Fluctuations of transverse increments in two-dimensional first passage percolation
Fluctuations of transverse increments in two-dimensional first passage percolation
复制标题
二维首通道渗流中横向增量的波动
DOI：
10.1214/22-ejp772
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发表时间：
2020
影响因子：
1.4
通讯作者：
Ujan Gangopadhyay
中科院分区：
文献类型：
--
作者：
Ujan Gangopadhyay
我们考虑了$\mathbb{Z}^2$上第一次通过渗流（FPP）的有限测地线，其中i.i.d.\具有指数矩的连续通过时间。正如文献中常见的那样，我们假设FPP模型满足某些基本性质，并从这些性质中推导出关于通过时间横向增量的结果。假设的性质大致如下：（i）通过时间在尺度r上的标准差为某个量级的sigma（r），$\left\{\sigma（r），r > 0\right\}$近似以r的幂增长：（ii）通过时间分布的尾部在尺度r上满足指数界，在r上一致;极限形状边界在某个固定方向$\theta$的邻域内具有从$0$和$\infty$一致有界的曲率。横向增量是指从原点到两个点$\boldsymbol{a}$和$\boldsymbol{B}$的通过时间之差，这两个点大约在原点的方向$\theta$上，并且$\boldsymbol{a}$和$\boldsymbol{B}$之间的方向是在方向$\theta$上极限形状的切线方向。主要的推论是，如果$\sigma（r）$对于某些$\chi>0$随$r^\chi$变化，且$\xi$使得$\chi=2\xi-1$，则位于距离$r$的两点之间的横向增量的大小为$r^{\chi/\xi}$的数量级。
We consider finite geodesics for first passage percolation (FPP) on $\mathbb{Z}^2$ with i.i.d.\ continuous passage times having exponential moments. As has been common in the literature, we assume that the FPP model satisfies certain basic properties conjectured to be true, and derive consequences about transverse increments of passage times from these properties. The assumed properties are approximately as follows: (i) the standard deviation of the passage time on scale $r$ is of some order $\sigma(r)$, with $\left\{\sigma(r), r > 0\right\}$ growing approximately as a power of $r$; (ii) the tails of the passage time distributions for distance $r$ satisfy an exponential bound on scale $\sigma(r)$, uniformly over $r$; and (iii) the limit shape boundary has curvature uniformly bounded away from $0$ and $\infty$ in a neighborhood of some fixed direction $\theta$. By transverse increment we mean the difference between passage times from the origin to two points $\boldsymbol{a}$ and $\boldsymbol{b}$ which are approximately in the direction $\theta$ from origin and the direction between $\boldsymbol{a}$ and $\boldsymbol{b}$ is the direction of the tangent to the limit shape at the direction $\theta$. The main consequences derived is that, if $\sigma(r)$ varies as $r^\chi$ for some $\chi>0$, and $\xi$ is such that $\chi=2\xi-1$, then magnitude of the transverse increment between two points situated at distance $r$ from each other is of the order of $r^{\chi/\xi}$.
通过自举的一般最后通道渗透的最佳尾部指数
影响因子：
2
作者：
Ganguly, Shirshendu;Hegde, Milind
通讯作者：
Hegde, Milind
影响因子：
2.4
作者：
Riddhipratim Basu;C. Hoffman;A. Sly
通讯作者：
Riddhipratim Basu;C. Hoffman;A. Sly