标题： 时间-时间协方差对于具有通用初始轮廓的最后通过渗流 显示英文标题

标题： Time-time covariance for last passage percolation with generic initial profile

摘要： 我们考虑在特征线附近的1+1维KPZ生长的时间相关性。 我们证明了在滴状、平面和稳态初始轮廓下的协方差收敛性。 特别是，这为[SIGMA 12 (2016), 074]中获得的稳态情况下的协方差精确公式提供了严格的证明。 此外，当两个观测时间接近时，我们证明了第一阶修正的普遍性，并提供了误差项的严格界。 该结果也适用于非必然稳态的随机初始轮廓。 显示英文摘要

摘要： We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [SIGMA 12 (2016), 074]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary.