3-5 August 2022
Universität Klagenfurt
Europe/Vienna timezone

Maximum interpoint distance of high-dimensional random vectors

4 Aug 2022, 10:00
HS 3 (Universität Klagenfurt)

HS 3

Universität Klagenfurt

Talk Stochastics Session A3 Stochastics


A limit theorem for the largest interpoint distance of $p$ i.i.d. points on $\mathbb R^n$ to the Gumbel distribution is proven, where the number of points $p=p_n$ tends to infinity as the dimension of the points $n$ tends to infinity. The theorem holds under moment assumptions and corresponding assumptions on the rate of $p$. The proof is based on the Chen-Stein Poisson approximation method and uses the sum structure of the interpoint distances. Therefore, an asymptotic distribution of a more general object is derived.

Primary author

Carolin Kleemann (Ruhr University Bochum)


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