Mathematical analysis reveals asymptotic dimension bounds of random simplicial complexes across sparse and dense regimes, advancing extreme value theory in random geometry.
The dimension of random simplicial complexes (defined as the maximal dimension among all faces) is a natural extreme value associated with the complex, and is closely related to other functionals defined by a maximum, such as the clique number of geometric graphs or scan statistics. We extend existing results in the binomial point process case to the Poisson setting in sparse graphs, give new ones about expectations and large deviation principles in all regimes, as well as give a first precise distribution result in the dense case.
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Kinga Nagy (2026) studied this question.
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