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arXiv · 1909.12322

How long is the convex minorant of a one-dimensional random walk?

Gerold Alsmeyer·Zakhar Kabluchko·Alexander Marynych·Vladislav Vysotsky
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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.

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Gerold Alsmeyer, Zakhar Kabluchko, Alexander Marynych, Vladislav Vysotsky. 2019-09-26. How long is the convex minorant of a one-dimensional random walk?. https://doi.org/10.1214/20-ejp497

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