Point processes in general position |
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Authors: | H Zessin |
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Institution: | 1. Universit?t Bielefeld, Bielefeld, Germany
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Abstract: | The aim of this note is to introduce for point processes in ? d the notions general position and reinforced general position, and to characterize these processes. As a consequence we show that Poisson processes P ρ with an infinite intensity measures ρ are in general position iff ρ is diffuse in the sense that any affine subspace of dimension d ? 1 is a ρ-nullset. Moreover, P ρ is in reinforced general position iff in addition any (d ? 1)-sphere is a ρ-nullset. |
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Keywords: | Point processes general positions physical clusters |
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