论文标题
几何方法，用于使Hadamard歧管的措施进行主要措施
Geometric Approach For Majorizing Measures on Hadamard Manifolds
论文作者
论文摘要
高斯工艺可以视为标准希尔伯特空间的子集，但是，随机过程的基础索引空间与其凸面船体之间的体积尺寸关系尚不清楚。对这种数量关系关系的理解可以帮助我们通过几何来建立主要的度量定理。在本文中，我们假设随机过程的基本索引空间是一个简单连接的歧管，其截面曲率小于负小于负（Hadamard歧管）。我们得出了基础索引空间的体积与其凸壳体积之间的比率。然后，我们应用此体积比以几何形式证明了主要量度定理。
Gaussian processes can be treated as subsets of a standard Hilbert space, however, the volume size relation between the underlying index space of random processes and its convex hull is not clear. The understanding of such volume size relations can help us to establish a majorizing measure theorem geometrically. In this paper, we assume that the underlying index space of random processes is a simply connected manifold with sectional curvature less than negative one (Hadamard manifold). We derive the upper bound for the ratio between the volume of the underlying index space and the volume of its convex hull. We then apply this volume ratio to prove the majorizing measure theorem geometrically.
