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Angular asymptotics for random walks

López Hernández, Alejandro and Wade, Andrew R. (2021) 'Angular asymptotics for random walks.', in A Lifetime of Excursions Through Random Walks and Lévy Processes. , pp. 315-342. Progress in Probability., 78


We study the set of directions asymptotically explored by a spatially homogeneous random walk in d-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some examples. We also explore links to the asymptotics of one-dimensional projections, and to the growth of the convex hull of the random walk.

Item Type:Book chapter
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Publisher statement:This a post-peer-review, pre-copyedit version of a chapter published in A Lifetime of Excursions Through Random Walks and Lévy Processes. The final authenticated version is available online at:
Date accepted:26 March 2021
Date deposited:09 August 2021
Date of first online publication:30 July 2021
Date first made open access:30 July 2022

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