指数最后通行渗流中Busemann函数的负相关性
Negative association of Busemann functions in exponential last-passage percolation
浏览论文内容
中文总结 AI 辅助
本文研究指数最后通行渗流中Busemann增量的相关性，发现其呈负相关性，利用指数权重特有的Burke性质推导了扩散尺度下Busemann增量和的指数集中不等式。
中文摘要 AI 辅助
可精确求解的KPZ随机增长模型的一个标志性特征是乘积形式不变测度。在指数最后通行渗流（LPP）的设定下，这对应于沿任意右下路径的Busemann增量相互独立。然而，当同时考虑多个渐近方向时，这种独立性会被打破，原因是联合不变测度并非联合乘积形式。本文表明，独立性的失效是单向的：任意方向上的Busemann增量呈负相关性。作为应用，我们推导了扩散尺度下Busemann增量和的指数集中不等式，即使这些增量不独立。尽管我们的论证依赖于指数权重特有的Burke性质，但所有其他证明要素——包括隐式的LPP单调性和排队映射的辫关系——对任意权重均成立。
英文摘要
One hallmark of exactly solvable KPZ random growth models is product-form invariant measures. In the setting of exponential last-passage percolation (LPP), this corresponds to the independence of Busemann increments along any down-right path. However, this independence breaks down when multiple asymptotic directions are considered simultaneously, owing to the fact that jointly invariant measures are not jointly product-form. This paper shows that the failure of independence is one-sided: Busemann increments across arbitrary directions are negatively associated. As an application, we derive an exponential concentration inequality for sums of Busemann increments on the diffusive scale, even when the increments are not independent. While our argument relies on a Burke property that is special to exponential weights, all other proof ingredients$\unicode{x2014}$including hidden LPP monotonicities and braid relations for queueing maps$\unicode{x2014}$hold for arbitrary weights.
