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Weighted halfspace depth

Daniel Hlubinka, Lukáš Kotík, Ondřej Vencálek (2010)

Kybernetika

Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

Windings of planar random walks and averaged Dehn function

Bruno Schapira, Robert Young (2011)

Annales de l'I.H.P. Probabilités et statistiques

We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

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