AI 中文总结
该研究针对上尾条件下的指数型定向最后通行渗流，确定了特定空间区域内及边界的单点涨落规律，扩展了相关工作，并通过串联队列对应关系揭示了非典型离站对网络其他位置的影响。
AI 中文摘要
我们研究在指定宏观点的最后通行时间为非典型大值条件下的指数型定向最后通行渗流，确定了该条件下产生的三个空间区域中两个区域内以及区域边界上的单点涨落，扩展了Baik-Cordaro-Tripathi的工作。根据观测点的位置，极限涨落由GUE Tracy-Widom分布、高斯分布或区域边界上的单峰BBP分布控制。通过与串联队列的对应关系，我们的结果还描述了某一顾客-站点对处非典型延迟离站如何影响网络中其他位置的离站时刻。
英文摘要
We study exponential directed last passage percolation conditioned on the last passage time to a specified macroscopic point being atypically large. We determine the one-point fluctuations throughout two of the three spatial regions arising under this conditioning, as well as on the boundaries between these regions, extending the work of Baik-Cordaro-Tripathi. Depending on the location of the observation point, the limiting fluctuations are governed by the GUE Tracy-Widom distribution, a Gaussian distribution, or the one-spike BBP distribution on the boundaries between these regions. Through the correspondence with tandem queues, our results also describe how an atypically late departure at one customer-station pair affects departure epochs elsewhere in the network.
Comments46 pages
