1 9 Fe b 20 07 Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
نویسندگان
چکیده
We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sample. The approach involves introducing a generalized spatial birth growth process allowing for cell overlap.
منابع مشابه
Brownian Limits, Local Limits and Variance Asymptotics for Convex Hulls in the Ball by Pierre Calka,
Schreiber and Yukich [Ann. Probab. 36 (2008) 363–396] establish an asymptotic representation for random convex polytope geometry in the unit ball Bd , d ≥ 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the par...
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