Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

Thomas, Andrew M.; Owada, Takashi

doi:10.1007/s10687-021-00419-1

Extremes

2021

DOI: 10.1007/s10687-021-00419-1

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Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

Andrew M. Thomas

Takashi Owada

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Cited by 3 publications

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Extremal linkage networks

Heydenreich

Hirsch

2021

Extremes

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We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with max-stable distribution. The fitness determines the node attractiveness w.r.t. incoming edges as well as the spatial range for outgoing edges. For max-stable fitness distributions, we thus obtain a complex spatial network, which we coin extremal linkage network.

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Extremal linkage networks

Heydenreich

Hirsch

2021

Extremes

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Functional strong law of large numbers for Betti numbers in the tail

Owada

Wei

2022

Extremes

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Central limit theorems and asymptotic independence for local U-statistics on diverging halfspaces

Thomas

2023

Bernoulli

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Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

Cited by 3 publications

References 21 publications

Extremal linkage networks

Extremal linkage networks

Functional strong law of large numbers for Betti numbers in the tail

Central limit theorems and asymptotic independence for local U-statistics on diverging halfspaces

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