论文标题
静止的最后一个通道渗透的中度偏差和退出时间估计
Moderate deviation and exit time estimates for stationary Last Passage Percolation
论文作者
论文摘要
我们考虑平面固定指数的最后一次通用渗透在带边界重量的正象限中。对于$ρ\ in（0,1）$和点$ v_n =（（（1-ρ）^2 n，ρ^2 n）$沿特征方向沿无限端，我们建立了右尾估计，并具有最佳的指数，用于大地测量时间的出口时间，以及用于段落中段偏差偏差的最佳指数估计。对于固定模型中的情况$ρ= \ frac {1} {2} $，我们在通道时间的下尾部建立了最佳指数的下限估计。我们的论点基于对点对点和点对上指数的上一段渗透的中等偏差估计，这些估计是通过随机矩阵估计获得的。
We consider planar stationary exponential Last Passage Percolation in the positive quadrant with boundary weights. For $ρ\in (0,1)$ and points $v_N=((1-ρ)^2 N,ρ^2 N)$ going to infinity along the characteristic direction, we establish right tail estimates with the optimal exponent for the exit time of the geodesic, along with optimal exponent estimates for the upper tail moderate deviations for the passage time. For the case $ρ=\frac{1}{2}$ in the stationary model, we establish the lower bound estimate with the optimal exponent for the lower tail of the passage time. Our arguments are based on moderate deviation estimates for point-to-point and point-to-line exponential Last Passage Percolation which are obtained via random matrix estimates.
