Isaev, M., Rodionov, I., Zhang, R.-R. et al. (1 more author) (2024) Extremal independence in discrete random systems. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 60 (4). pp. 2923-2944. ISSN 0246-0203
Abstract
Let X(n) ∈ Rd be a sequence of random vectors, where n ∈ N and d = d(n). Under certain weakly dependence conditions, we prove that the distribution of the maximal component of X and the distribution of the maximum of their independent copies are asymptotically equivalent. Our result on extremal independence relies on new lower and upper bounds for the probability that none of a given finite set of events occurs. As applications, we obtain the distribution of various extremal characteristics of random discrete structures such as maximum codegree in binomial random hypergraphs and the maximum number of cliques sharing a given vertex in binomial random graphs. We also generalise Berman-type conditions for a sequence of Gaussian random vectors to possess the extremal independence property.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 Association des Publications de l’Institut Henri Poincaré. This is an author-produced version of a paper subsequently published in Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Extreme value theory; Limit theorems; Random graphs; Gaussian vectors; Berman condition |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 Mar 2025 09:15 |
Last Modified: | 25 Mar 2025 09:15 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/23-aihp1402 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:224781 |