Abstract
A crinkled subordinator is an ℓ2-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→∞.
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