How long is the convex minorant of a one-dimensional random walk?
Probability
2020-08-14 v2
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.
Cite
@article{arxiv.1909.12322,
title = {How long is the convex minorant of a one-dimensional random walk?},
author = {Gerold Alsmeyer and Zakhar Kabluchko and Alexander Marynych and Vladislav Vysotsky},
journal= {arXiv preprint arXiv:1909.12322},
year = {2020}
}
Comments
21 pages, 1 figure, to appear in the Electronic Journal of Probability