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Clusters in one-dimensional Poissonian distributions of points: Exact approach.

We present a rigorous approach to the problem of the random clustering of points in one-dimensional Poissonian distributions. Exact expressions for the probability density of clusters are derived, and the statistical properties of the inner configuration of their associated structures are studied in detail. We review previous works in the field, assessing their accuracy in the context of the present approach. Its extension to more general distributions is pointed out, and several of the many practical applications of these works are briefly recalled