发表机构
University of Geneva（日内瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明布朗末次通过渗流在奥恩斯坦-乌伦贝克动力学下存在有向景观上的非平凡连续平稳可逆子序列极限，通过强通过时间稳定性与端点正则性建立紧性，并利用分数重叠趋于1论证非平凡性。
AI 中文摘要
我们证明了在奥恩斯坦-乌伦贝克动力学下，布朗末次通过渗流的子序列尺度极限存在一个有向景观上的非平凡连续平稳可逆动力学。来自配套论文Bhatia '26的强通过时间稳定性估计，结合静态端点正则性，给出了在临界动力学尺度$n^{-1/3}$下的紧性。为建立子序列极限动力学的非平凡性，我们证明在动力学BLPP中，时间零和$a n^{-1/3}$时刻测地线之间的分数重叠在首先$n\to\infty$然后$a\downarrow0$时趋于1。该证明细化了Ganguly-Hammond '24的游走论证，使用了强通过时间稳定性以及固定动力学时间在更细空间尺度下日益次临界的事实。
英文摘要
We prove the existence of a non-trivial continuous stationary reversible dynamics on the directed landscape as a subsequential scaling limit of Brownian last passage percolation under the Ornstein--Uhlenbeck dynamics. Strong passage-time stability estimates from the companion paper Bhatia '26, together with static endpoint regularity, give tightness at the critical dynamical scale $n^{-1/3}$. To establish non-triviality of the subsequential limiting dynamics, we show that, in dynamical BLPP, the fractional overlap between geodesics at times zero and $a n^{-1/3}$ tends to one as first $n\to\infty$ and then $a\downarrow0$. The proof refines the excursion argument of Ganguly-Hammond '24, using strong passage-time stability and the fact that a fixed dynamical time is increasingly subcritical at finer spatial scales.
Comments48 pages, 10 figures
