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A one-dimensional Poisson growth model non-overlapping intervals

Daley, Daryl; Mallows, C; Shepp, Lawrence


Suppose given a realization of a Poisson process on the line: call the points 'germs' because at a given instant 'grains' start growing around every germ, stopping for any particular grain when it touches another grain. When all growth stops a fraction e-1 of the line remains uncovered. Let n germs be thrown uniformly and independently onto the circumference of a circle, and let grains grow under a similar protocol. Then the expected fraction of the circle remaining uncovered is the nth partial...[Show more]

CollectionsANU Research Publications
Date published: 2000
Type: Journal article
Source: Stochastic Processes and their Applications


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