Translator Disclaimer
2020 How long is the convex minorant of a one-dimensional random walk?
Gerold Alsmeyer, Zakhar Kabluchko, Alexander Marynych, Vladislav Vysotsky
Electron. J. Probab. 25(none): 1-22 (2020). DOI: 10.1214/20-EJP497

Abstract

We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit distributions for this length. Among other tools, a representation of the convex minorant of a random walk in terms of uniform random permutations is utilized.

Citation

Download Citation

Gerold Alsmeyer. Zakhar Kabluchko. Alexander Marynych. Vladislav Vysotsky. "How long is the convex minorant of a one-dimensional random walk?." Electron. J. Probab. 25 1 - 22, 2020. https://doi.org/10.1214/20-EJP497

Information

Received: 26 September 2019; Accepted: 23 July 2020; Published: 2020
First available in Project Euclid: 5 September 2020

zbMATH: 07252699
MathSciNet: MR4147518
Digital Object Identifier: 10.1214/20-EJP497

Subjects:
Primary: 60F05, 60G55
Secondary: 60J10

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.25 • 2020
Back to Top