 Random walks in the high-dimensional limit II: The crinkled subordinatorZakhar Kabluchko, Alexander Marynych and Kilian Raschel Stochastic Processes and their Applications, 2024, vol. 176, issue C 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→∞. Keywords: Crinkled arc; Gromov–Hausdorff convergence; Hausdorff distance up to isometry; High-dimensional limit; Random metric space; Random walk; Subordinator; Wiener spiral (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001340 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104428 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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