Discrete Spacings
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 $1, 2,..., k1$ have simultaneously a limiting normal distribution as $n\to\infty$. This is proved by the classical method of moments.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:math/0112056
 Bibcode:
 2001math.....12056K
 Keywords:

 Probability;
 Classical Analysis and ODEs;
 60F05
 EPrint:
 14 pages