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Alsmeyer, Gerold, Kabluchko, Zakhar, Marynych, Alexander V and Vysotsky, Vladislav (2020) How long is the convex minorant of a one-dimensional random walk? Electronic Journal of Probability, 25 (a105). pp. 1-22. ISSN 1083-6489
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Official URL: https://dx.doi.org/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.
Item Type: | Article |
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Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Related URLs: | |
SWORD Depositor: | Mx Elements Account |
Depositing User: | Mx Elements Account |
Date Deposited: | 07 Aug 2020 09:58 |
Last Modified: | 07 Sep 2020 14:00 |
URI: | http://sro.sussex.ac.uk/id/eprint/92972 |
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