On Tournaments and Negative Dependence

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https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-tournaments-and-negative-dependence/A58CEE28D991F16DD6766E7C9664225E

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https://doi.org/10.1017/jpr.2022.104
 http://hdl.handle.net/11603/25171

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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Author/Creator ORCID

https://orcid.org/0000-0003-2888-674X

Date

2023-02-07

Type of Work

journal articles
preprints
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Citation of Original Publication

Malinovsky, Yaakov, and Yosef Rinott. “On Tournaments and Negative Dependence.” Journal of Applied Probability 60, no. 3 (September 2023): 945–54. https://doi.org/10.1017/jpr.2022.104.

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This article has been published in a revised form in Journal of Applied Probability https://doi.org/10.1017/jpr.2022.104. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust.

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Abstract

Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations, the rate of increase of the maximum, and more. In the study of probability models of tournaments, negative dependence of participants' outcomes arises naturally with application to various asymptotic results. In particular, the property of negative orthant dependence was proved in several articles for different tournament models, with a special proof for each model. In this note we unify these results by proving a stronger property, negative association, a generalization leading to a very simple proof. We also present a natural example of a knockout tournament where the scores are negatively orthant dependent but not negatively associated. The proof requires a new result on a preservation property of negative orthant dependence that is of independent interest.