论文标题
猫（0）空间的中央限制定理，带有缩合等法
Central limit theorem on CAT(0) spaces with contracting isometries
论文作者
论文摘要
让$ g $为适当的猫（0）空间$ x $的非元素动作的集团，让$μ$成为$ g $的措施，以便由$μ$生成的随机步行$（z_n）_n $在$ x $上具有有限的第二刻。让$ o $成为$ x $的基础，并假设存在$ g $的等级等级。我们证明，在这种情况下，$（z_n o）_n $满足了中心限制定理，即随机变量$ \ frac {1} {\ sqrt {n}}}（d（d（z_n o，o）-nλ）$在法律中收集到非分数g的$ n___ $ $ $ $ $ $ $ c的随机分布。该策略依赖于H. Petyt，A。Zalloum和D. spriano引入的双曲线模型的使用，它们是曲线图和CAT（0）空间类别的Cubical超平面的类似物。作为一方面的结果，我们证明了nth step $ z_n $在$ x $上作用的概率作为承包等轴测图，为1 $ n $转到无限。
Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $μ$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $μ$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and assume that there exists a rank one isometry in $G$. We prove that in this context, $(Z_n o )_n$ satisfies a Central Limit Theorem, namely that the random variables $\frac{1}{\sqrt{n}}(d(Z_n o, o) - n λ) $ converge in law to a non-degenerate Gaussian distribution $N_μ$, for $λ$ the (positive) drift of the random walk. The strategy relies on the use of hyperbolic models introduced by H. Petyt, A. Zalloum and D. Spriano, which are analogues of curve graphs and cubical hyperplanes for the class of CAT(0) spaces. As a side result, we prove that the probability that the nth-step $Z_n$ acts on $X$ as a contracting isometry goes to 1 as $n$ goes to infinity.
