Isaev, Mikhail and Rodionov, Igor and Zhang, Rui-Ray and Zhukovskii, Maxim (2024) Extremal independence in discrete random systems. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 60 (4). pp. 2923-2944. DOI https://doi.org/10.1214/23-AIHP1402
Isaev, Mikhail and Rodionov, Igor and Zhang, Rui-Ray and Zhukovskii, Maxim (2024) Extremal independence in discrete random systems. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 60 (4). pp. 2923-2944. DOI https://doi.org/10.1214/23-AIHP1402
Isaev, Mikhail and Rodionov, Igor and Zhang, Rui-Ray and Zhukovskii, Maxim (2024) Extremal independence in discrete random systems. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 60 (4). pp. 2923-2944. DOI https://doi.org/10.1214/23-AIHP1402
Abstract
Let X(n) in R^d be a sequence of random vectors, where n in 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.
Item Type: | Article |
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Uncontrolled Keywords: | Berman condition; Extreme value theory; Gaussian vectors; limit theorems; Random graphs |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 01 May 2025 13:11 |
Last Modified: | 01 May 2025 13:11 |
URI: | http://repository.essex.ac.uk/id/eprint/36205 |