发表机构
University of Pennsylvania; University of Michigan（宾夕法尼亚大学; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文研究指数定向最后通过渗流在单点上大偏差事件下的条件模型，提出条件极限形状的预测并证明波动结果，发现对角线附近波动由共享高斯分量的布朗桥描述。
AI 中文摘要
指数定向最后通过渗流是一种随机最大化模型，与串联队列和相互作用粒子系统相关。我们研究该渗流的线到点模型，其中起点允许在线边界内变化，并以固定终点的异常大的最后通过时间为条件。扩展最近关于起点固定的点到点模型的结果，我们为条件极限形状提出启发式预测，并通过精确多点公式的陡降分析证明了某些区域中的相应波动结果。我们的计算表明，对角线附近的条件波动由通过额外共享高斯分量耦合的布朗桥描述。
英文摘要
Exponential directed last passage percolation is a random maximization model connected to tandem queues and interacting particle systems. We study the line-to-point model of the percolation, in which the starting point is allowed to vary inside a line boundary, conditioned on an atypically large last-passage time to a fixed endpoint. Extending recent results for the point-to-point model where the starting point is fixed, we develop heuristic predictions for the conditional limit shape and prove corresponding fluctuation results in certain regimes through steepest-descent analysis of exact multi-point formulas. Our calculations suggest that the conditional fluctuations near diagonal are described by Brownian bridges coupled through an additional shared Gaussian component.
