A one-dimensional Poisson growth model non-overlapping intervals
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]
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|Source:||Stochastic Processes and their Applications|
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