论文标题
属性（t）在密度高于1/3的双曲线组随机商中
Property (T) in random quotients of hyperbolic groups at densities above 1/3
论文作者
论文摘要
我们研究了Gromov密度模型中固定的非元素双曲线群的随机商。令$ g = \ langle s \; \ vert \; t \ rangle $是非元素双曲线组的有限陈述，让$ ann_ {l，ω}（g）$是$ l-ω（l）$和$ l $ in $ g $ in $ g $之间的规范元素的集合。在密度$ d $和长度$ω$ -near $ l $的密度下随机商是通过杀死一组均匀随机选择的$ \ vert s_ {l}（g）\ vert ^{d} $单词$ ann_ {l，ω（l）}（l）}（g）$，$ and）$ pert ^{d} $ wiste $ n $ and = Oph（l）（l）= o__ p}（l}（l）。我们证明，对于任何d> 1/3，这样的商具有属性（t），概率趋于$ 1 $ as $ l $倾向于无限。该结果回答了gromov的问题 - 散布，并加强了› kotowski-kotowski的定理。
We study random quotients of a fixed non-elementary hyperbolic group in the Gromov density model. Let $G=\langle S\;\vert\; T\rangle $ be a finite presentation of a non-elementary hyperbolic group, and let $Ann_{l,ω}(G)$ be the set of elements of norm between $l-ω(l)$ and $l$ in $G$. A random quotient at density $d$ and length $ω$-near $l$ is defined by killing a uniformly randomly chosen set of $\vert S_{l}(G)\vert ^{d}$ words in $Ann_{l,ω(l)}(G)$, where $ω(l) =o_{l}(l)$. We prove that for any d>1/3, such a quotient has Property (T) with probability tending to $1$ as $l$ tends to infinity. This result answers a question of Gromov--Ollivier and strengthens a theorem of Żuk (c.f Kotowski--Kotowski).
