Lehigh University

most citedGaussian limits for random measures in geometric probability

107 citations

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math.PR2007★ 46 cited

Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points

T. Schreiber, J. E. Yukich

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 z…

math.PR2005★ 4 cited

Singularity points for first passage percolation

J. E. Yukich, Yu Zhang

Let $0 < a < b < \infty$ be fixed scalars. Assign independently to each edge in the lattice $Z^{2}$ the value $a$ with probability $p$ or the value $b$ with probability $1 - p$ . For…

math.PR2005★ 107 cited

Gaussian limits for random measures in geometric probability

Yu. Baryshnikov, J. E. Yukich

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional wh…