Work

Longest k-monotone chains

Year: 2020

Type: article

Abstract: We study higher order convexity properties of random point sets in the unit square. Given $n$ uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in $k$-monotone position, subject to mild boundary conditions. Besides determining the order of magnitude of the expectation, we also prove strong concentration estimates. We provide a general framework that includes the previously studied cases of $k=1$ (longest increasing sequences) and $k=2$ (longest convex chains).

Source: Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)

DOI: 10.48550/arxiv.2009.13887

Author: Ambrus, Gergely

Institution: HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3090198134

FWCI:

Cites: 19

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Related to: 10