标题： 高维极限中的随机游走 II：皱褶次过程 显示英文标题

标题： Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator

摘要： 一个褶皱子序器是一个取值为$\ell^2$的随机过程，可以认为是通常的一维子序器的一种版本，其中每个可数多个跳跃的方向都与其他所有跳跃的方向正交。 我们证明，具有$d$维的随机游走，其$n$个独立同分布的步长，径向分量具有重尾分布，而角度分量渐近正交，当$d,n\to\infty$时，在保距意义下路径在Hausdorff距离中以分布方式收敛，并且在作为随机度量空间观察时，也在Gromov--Hausdorff意义上收敛到褶皱子序器的闭合范围。 显示英文摘要

摘要： A crinkled subordinator is an $\ell^2$-valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps being in a direction orthogonal to the directions of all other jumps. We show that the path of a $d$-dimensional random walk with $n$ independent identically distributed steps with heavy-tailed distribution of the radial components and asymptotically orthogonal angular components converges in distribution in the Hausdorff distance up to isometry and also in the Gromov--Hausdorff sense, if viewed as a random metric space, to the closed range of a crinkled subordinator, as $d,n\to\infty$.