论文标题
均匀扩展随机步行
Uniformly Expanding Random Walks on Manifolds
论文作者
论文摘要
在本文中，我们在平滑的歧管上统一构建随机步行。在较高的维度中，我们对统一扩展的定义衡量了子空间的生长，而不是单个向量的生长。波特里（Potrie）表明，给定任何开放式$ u $ of $ \ text {diff}^\ infty_ {vol}（\ mathbb {t}^2）$，存在于$ u $的有限子集中支持的一致扩展的随机步行$ $。在本文中，我们将这些结果扩展到任何维度的封闭歧管，建立在Potrie和Chung的工作的基础上，以建立强大的示例类。
In this paper we construct uniformly expanding random walks on smooth manifolds. In higher dimensions, our definition of uniform expansion measures the growth of subspaces rather than single vectors. Potrie showed that given any open set $U$ of $\text{Diff}^\infty_{vol}(\mathbb{T}^2)$, there exists an uniformly expanding random walk $μ$ supported on a finite subset of $U$. In this paper we extend those results to closed manifolds of any dimension, building on the work of Potrie and Chung to build a robust class of examples.
