论文标题
随机步行交叉点的大偏差
Large Deviations for Intersections of Random Walks
论文作者
论文摘要
我们证明了两个独立无限时间范围在五个及以上的两个独立无限时间范围的相交数量的巨大偏差原理，从而改善了Khanin，Mazel，Mazel，Shlosman和Sina { ^ï} [KMSS94]。在离散的环境中，这是一个猜想的范·丹·伯格（Van Den Berg），博尔瑟森（Bolthausen）和丹·霍兰德（Den Hollander）[BBH04]，后者分析了有限时间地平线的Wiener香肠的这个问题。该证明是基于其结果的（在Phetpradap [Phet12]的离散设置中恢复了），并将其与作者最新作品中开发的一系列工具相结合[AS17，AS19A，AS20]。此外，我们表明大多数交叉路口都发生在一个盒子中，在一个盒子中，这两个步行都意识到了一个秩序的职业密度。
We prove a Large Deviations Principle for the number of intersections of two independent infinite-time ranges in dimension five and more, improving upon the moment bounds of Khanin, Mazel, Shlosman and Sina{ï} [KMSS94]. This settles, in the discrete setting, a conjecture of van den Berg, Bolthausen and den Hollander [BBH04], who analyzed this question for the Wiener sausage in finite-time horizon. The proof builds on their result (which was resumed in the discrete setting by Phetpradap [Phet12]), and combines it with a series of tools that were developed in recent works of the authors [AS17, AS19a, AS20]. Moreover, we show that most of the intersection occurs in a single box where both walks realize an occupation density of order one.
