Open Access
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: 1-22 (2020). DOI: 10.1214/20-EJP497


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.


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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.


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

Primary: 60F05 , 60G55
Secondary: 60J10

Keywords: convex minorant , random permutation , Random walk

Vol.25 • 2020
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