Discrete Spacings

2001/12/06 by Chris A. J. Klaassen, Klaassen, Chris A. J., J. Theo Runnenburg +1
Mathematics · #60F05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #math.CA #math.PR #msc:60F05

paper · pdf · doi:10.48550/arxiv.math/0112056

14 pages

arxiv created 2001/12/06 · arxiv updated 2009/11/30

Abstract

Consider a string of n positions, i.e. a discrete string of length n. Units of length k are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than k. When centered and scaled by n^-1/2 the resulting numbers of spacings of length 1, 2,..., k-1 have simultaneously a limiting normal distribution as n→∞. This is proved by the classical method of moments.

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