论文标题
灯塔对角线产品的庞加莱概况
Poincaré profiles of lamplighter diagonal products
论文作者
论文摘要
我们展示了有限生成的团体，具有规定的庞加莱概况。可以为$ n/\ log n $和线性之间的函数规定，并且对于函数至少$ n/（\ log \ log n）$很清晰。这些概况是由休ume，麦凯和泰塞拉在2019年引入的，作为对分离概况的概括，本杰米尼，施拉姆姆和蒂姆在2012年定义。所使用的群体家族基于布里塞尔和郑的建设。作为应用，我们表明存在渐近维度的有界度图，它们不会粗糙地嵌入有界度树的任何有限产物中，并且在$ l^p $ spaces中显示了任意大失真的图形的高限序列。
We exhibit finitely generated groups with prescribed Poincaré profiles. It can be prescribed for functions between $n/\log n$ and linear, and is sharp for functions at least $n/(\log\log n)$. Those profiles were introduced by Hume, Mackay and Tessera in 2019 as a generalization of the separation profile, defined by Benjamini, Schramm and Timár in 2012. The family of groups used is based on a construction of Brieussel and Zheng. As applications, we show that there exists bounded degrees graphs of asymptotic dimension one that do not coarsely embed in any finite product of bounded degrees trees, and exhibit hyperfinite sequences of graphs of arbitrary large distortion in $L^p$-spaces.
