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Sequential random displacements of points in an interval

Published online by Cambridge University Press:  14 July 2016

David Mannion
David Mannion*
Affiliation:
Royal Holloway College
*
∗ Postal address: Department of Statistics and Computer Science, Royal Holloway College, University of London, Egham, Surrey, TW20 0EX, U.K.
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Abstract

An array of points {Z1, Z2, …, Zn–1} in the interval V = [0, L], is such that 0 ≦ Z1, ≦ Z2 ≦ … ≦ Zn–1, ≦ L. One of the points is chosen at random (Zk, say, with probability pk) and displaced to a new position within the interval [Zk–1, Zk+ 1], the position again chosen at random according to a probability distribution Gk. We derive some results concerning the limiting distribution of the array after a succession of such displacements. If Gk is a uniform distribution, it appears that the number of displacements necessary to open up a gap between at least one pair of adjacent points of size at least γ is O(ρ n), n →∞, where ρ = L/(L – γ).

Keywords

RANDOM COMPLETE PACKINGRANDOM SPACE-FILLINGHARD-CORE MODELSSPATIAL COMPETITIONRANDOM PARTITIONSUNIFORM SPACINGSPARTICLE INTERACTIONSPATIAL INTERACTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 251 - 263
Copyright
Copyright © Applied Probability Trust 1983 

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References

Blaisdell, B. E. and Solomon, H. (1982) Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti. J. Appl. Prob. 19, 382–390.CrossRefGoogle Scholar
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