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2009.40: Intrinsic correlation in planar Poisson line processes

2009.40: CTJ Dodson and WW Sampson (2009) Intrinsic correlation in planar Poisson line processes. Applied Mathematics Letters, 22 (7). pp. 981-983. ISSN 0893-9659

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DOI: 10.1016/j.aml.2009.01.005

Abstract

The polygons arising from a planar Poisson line process have an exponential distribution of their side lengths and are known to be more regular as their area, perimeter or number of sides increase. Local regions with higher line density have smaller polygon side lengths and conversely. Numerical analysis of computer generated Poisson line processes shows that when pairs of adjacent polygon sides (x,y) are sorted such that x < y they are correlated with correlation coefficient ~ 0.616 as compared to 1/sqrt{5} ~ 0.447 for independent sorted exponential (x,y) pairs. This correlation is consistent with the observed regularity of polygons in realizations of planar Poisson line processes.

Item Type:Article
Uncontrolled Keywords:Poisson lines, random polygons, correlation, Monte Carlo
Subjects:MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2009.40
Deposited By:Prof CTJ Dodson
Deposited On:25 May 2009

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