Probabilities of filaments in a Poissonian distribution of points - I. Straight filaments

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Abstract
Statistical techniques are devised to assess the likelihood of a Poisson sample of points in two and three dimensions, containing specific filamentary structures. For that purpose, Otto et al.'s expression for the probability density of clumps in a Poissonian distribution of points is generalized for any value of the density contrast. A way of counting filaments differing from that of Otto et al. is proposed, because at low density contrast the filaments counted by Otto et al. are distributed in a clumpy fashion, each clump of filaments corresponding to a distinct observed filament.

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