Angular asymptotics for random walks

López Hernández, Alejandro; Wade, Andrew R.

doi:10.1007/978-3-030-83309-1_17

Angular asymptotics for random walks

López Hernández, Alejandro; Wade, Andrew R.

Authors

Alejandro López Hernández

Professor Andrew Wade andrew.wade@durham.ac.uk
Professor

Contributors

Loïc Chaumont
Editor

Andreas E. Kyprianou
Editor

Abstract

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.

Citation

López Hernández, A., & Wade, A. R. (2021). Angular asymptotics for random walks. In L. Chaumont, & A. E. Kyprianou (Eds.), A Lifetime of Excursions Through Random Walks and Lévy Processes (315-342). Springer Verlag. https://doi.org/10.1007/978-3-030-83309-1_17

Acceptance Date	Mar 26, 2021
Online Publication Date	Jul 30, 2021
Publication Date	2021
Deposit Date	Mar 24, 2021
Publicly Available Date	Jul 30, 2022
Publisher	Springer Verlag
Pages	315-342
Series Title	Progress in Probability
Series Number	78
Book Title	A Lifetime of Excursions Through Random Walks and Lévy Processes
ISBN	9783030833091
DOI	https://doi.org/10.1007/978-3-030-83309-1_17
Publisher URL	https://www.springer.com/gb/book/9783030833084

Files

Accepted Book Chapter (408 Kb)
PDF

Copyright 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: https://doi.org/10.1007/978-3-030-83309-1_17