Intrinsic correlation in planar Poisson line processes

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

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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 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Prof CTJ Dodson
Date Deposited: 25 May 2009
Last Modified: 20 Oct 2017 14:12

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