Angular asymptotics for random walks

López Hernández, Alejandro; Wade, Andrew R.

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

• 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
• Public URL: https://durham-repository.worktribe.com/output/1625749
• Publisher URL: https://www.springer.com/gb/book/9783030833084
• Contract Date: Mar 26, 2021