The average distance of the n-th neighbour in a uniform distribution of random points

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dc.creatorBhattacharyya, Pratip
dc.creatorChakrabarti, Bikas K.
dc.creatorChakraborti, Anirban
dc.date2001-04-09
dc.date2001-06-21
dc.date.accessioned2026-07-07T02:40:58Z
dc.date.available2026-07-07T02:40:58Z
dc.descriptionWe first review the derivation of the exact expression for the average distance $<r_n>$ of the n-th neighbour of a reference point among a set of N random points distributed uniformly in a unit volume of a D-dimensional geometric space. Next we propose a `mean-field\rq theory of $<r_n>$ and compare it with the exact result. The result of the `mean-field\rq theory is found to agree with the exact expression only in the limit $D \to \infty$ and $n \to \infty$. Thus the `mean-field\rq approximation is useless in this context.
dc.description6 pages, no figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0104139
dc.identifierhttp://arxiv.org/abs/cond-mat/0104139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/17574
dc.subjectStatistical Mechanics
dc.titleThe average distance of the n-th neighbour in a uniform distribution of random points
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