Since the year 2000, a concerted campaign against malaria has led to unprecedented levels of intervention coverage across sub-Saharan Africa. Understanding the effect of this control effort is vitalâ€¦ (More)

We establish Gaussian limits for measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the densityâ€¦ (More)

Let Bn be an increasing sequence of regions in d-dimensional space with volume n and with union d. We prove a general central limit theorem for functionals of point sets, obtained either byâ€¦ (More)

Statistics arising in geometric probability can often be expressed as sums of stabilizing functionals, that is functionals which satisfy a local dependence structure. In this note we show thatâ€¦ (More)

Nearest neighbor cells in Rd, d â‰¥ 1, are used to define coefficients of divergence (Ï†divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to convergeâ€¦ (More)

Schreiber and Yukich [Ann. Probab. 36 (2008) 363â€“396] establish an asymptotic representation for random convex polytope geometry in the unit ball Bd , d â‰¥ 2, in terms of the general theory ofâ€¦ (More)

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.â€¦ (More)

We consider the r th power quantization error arising in the optimal approximation of a d-dimensional probability measure P by a discrete measure supported by the realization of n i.i.d. randomâ€¦ (More)

Let 0 < a < b <âˆž be fixed scalars. Assign independently to each edge in the lattice Z2 the value a with probability p or the value b with probability 1 âˆ’ p. For all u,v âˆˆ Z2, let T (u, v) denote theâ€¦ (More)