We consider planar stationary exponential Last Passage Percolation in the positive quadrant with boundary weights. For $\rho\in (0,1)$ and points $v_N=((1-\rho)^2 N,\rho^2 N)$ 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 $\rho=\frac{1}{2}$ 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.

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固定最后通道渗透的中等偏差和退出时间估计

我们考虑具有边界权重的正象限中的平面平稳指数最后通道渗透。对于 $\rho\in (0,1)$ 和点 $v_N=((1-\rho)^2 N,\rho^2 N)$ 沿特征方向趋于无穷大，我们建立右尾估计测地线退出时间的最佳指数，以及通过时间的上尾中等偏差的最佳指数估计。对于平稳模型中 $\rho=\frac{1}{2}$ 的情况，我们使用通过时间下尾的最优指数建立下限估计。我们的论点基于点对点和点对线指数最后通道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。