在有向首达渗流中时间常数仅在渗流锥上消失
概率论
2008-03-10 v2
摘要
我们考虑 Z 2 {\bf Z}^2 Z 2 e e e F F F t ( e ) t(e) t ( e ) T ⃗ ( 0 , ( r , θ ) ) \vec{T}({\bf 0}, (r,\theta)) T ( 0 , ( r , θ )) ( r , θ ) (r, \theta) ( r , θ ) ( r , θ ) ∈ R + × [ 0 , π / 2 ] (r, \theta)\in {\bf R}^+\times [0,\pi/2] ( r , θ ) ∈ R + × [ 0 , π /2 ] T ⃗ ( 0 , ( r , θ ) ) / r \vec{T}({\bf 0}, (r, \theta))/r T ( 0 , ( r , θ )) / r μ ⃗ F ( θ ) \vec{\mu}_F (\theta) μ F ( θ ) p ⃗ c \vec{p}_c p c p ⃗ c \vec{p}_c p c F ( 0 ) < p ⃗ c F(0) < \vec{p}_c F ( 0 ) < p c 0 ≤ θ ≤ π / 2 0\leq \theta\leq \pi/2 0 ≤ θ ≤ π /2 μ ⃗ F ( θ ) > 0 \vec{\mu}_F(\theta) >0 μ F ( θ ) > 0 F ( 0 ) = p ⃗ c F(0) = \vec{p}_c F ( 0 ) = p c θ ≠ π / 4 \theta\neq \pi/4 θ = π /4 μ ⃗ F ( θ ) > 0 \vec{\mu}_F(\theta) >0 μ F ( θ ) > 0 F ( 0 ) = p > p ⃗ c F(0)=p > \vec{p}_c F ( 0 ) = p > p c θ p − \theta_p^- θ p − θ p + \theta_p^+ θ p + 0 ≤ θ p − < θ p + ≤ π / 2 0\leq \theta^-_p< \theta^+_p \leq \pi/2 0 ≤ θ p − < θ p + ≤ π /2 θ ∉ [ θ p − , θ p + ] \theta\not\in [\theta_p^-, \theta^+_p] θ ∈ [ θ p − , θ p + ] μ ⃗ ( θ ) > 0 \vec{\mu} (\theta) >0 μ ( θ ) > 0 θ ∈ [ θ p − , θ p + ] \theta\in [\theta_p^-, \theta^+_p] θ ∈ [ θ p − , θ p + ] T ⃗ ( 0 , ( r , θ ) ) \vec{T}({\bf 0}, (r, \theta)) T ( 0 , ( r , θ )) F F F p ⃗ c \vec{p}_c p c
引用
@article{arxiv.0802.3519,
title = {The time constant vanishes only on the percolation cone in directed first passage percolation},
author = {Yu Zhang},
journal= {arXiv preprint arXiv:0802.3519},
year = {2008}
}
备注
28 pages, 1 figure