# Limit theorems for critical first-passage percolation on the triangular lattice

@article{Yao2016LimitTF,
title={Limit theorems for critical first-passage percolation on the triangular lattice},
author={Chang-long Yao},
journal={arXiv: Probability},
year={2016}
}
Consider (independent) first-passage percolation on the sites of the triangular lattice $\mathbb{T}$. Denote the passage time of the site $v$ in $\mathbb{T}$ by $t(v)$, and assume that $P(t(v)=0)=P(t(v)=1)=1/2$. Denote by $b_{0,n}$ the passage time from 0 to the halfplane $\{v\in\mathbb{T}:\mbox{Re}(v)\geq n\}$, and by $T(0,nu)$ the passage time from 0 to the nearest site to $nu$, where $|u|=1$. We prove that as $n\rightarrow\infty$, $b_{0,n}/\log n\rightarrow 1/(2\sqrt{3}\pi)$ a.s., $E[b_{0,n… Expand 12 Citations Asymptotics for 2D critical and near-critical first-passage percolation We study Bernoulli first-passage percolation (FPP) on the triangular lattice in which sites have 0 and 1 passage times with probability p and $$1-p$$1-p, respectively. Denote by$${\mathcalExpand Universality of the time constant for$2D$critical first-passage percolation. • Mathematics • 2019 We consider first-passage percolation (FPP) on the triangular lattice with vertex weights$(t_v)$whose common distribution function$F$satisfies$F(0)=1/2$. This is known as the critical case ofExpand Critical first-passage percolation starting on the boundary • Mathematics • Stochastic Processes and their Applications • 2019 Abstract We consider first-passage percolation on the two-dimensional triangular lattice T . Each site v ∈ T is assigned independently a passage time of either 0 or 1 with probability 1 ∕ 2 . DenoteExpand First passage percolation on crystal lattices This paper studies the first passage percolation (FPP) model: each edge in the cubic lattice is assigned a random passage time, and consideration is given to the behavior of the percolation regionExpand Empirical distributions, geodesic lengths, and a variational formula in first-passage percolation. This article resolves, in a dense set of cases, several open problems concerning geodesics in i.i.d. first-passage percolation on$\mathbb{Z}^d\$. Our primary interest is in the empirical measures ofExpand
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