论文标题
正面树木中流行差异的直接和逆结果
Direct and inverse results for popular differences in trees of positive dimension
论文作者
论文摘要
我们为结果树建立了类似物，与集合$ e \ subset \ mathbb {n} $的密度，其一组流行差异的密度以及$ e $的结构相关。为了获得我们的结果，我们将Furstenberg和Weiss的对应原理形式化，该原理将树上的组合数据与Markov过程的动力学联系起来。我们的主要工具是用于衡量测量系统中的返回时间的旋转型逆定理。在奇异环境中，我们使用了Björklund和Shkredov的第一作者的最新结果以及稳定性型扩展（与Shkredov共同证明）；我们还证明了非共性系统的新结果。
We establish analogues for trees of results relating the density of a set $E \subset \mathbb{N}$, the density of its set of popular differences, and the structure of $E$. To obtain our results, we formalise a correspondence principle of Furstenberg and Weiss which relates combinatorial data on a tree to the dynamics of a Markov process. Our main tools are Kneser-type inverse theorems for sets of return times in measure-preserving systems. In the ergodic setting we use a recent result of the first author with Björklund and Shkredov and a stability-type extension (proved jointly with Shkredov); we also prove a new result for non-ergodic systems.
