2,314 research outputs found
Intrinsic volumes of inscribed random polytopes in smooth convex bodies
Let be a dimensional convex body with a twice continuously
differentiable boundary and everywhere positive Gauss-Kronecker curvature.
Denote by the convex hull of points chosen randomly and independently
from according to the uniform distribution. Matching lower and upper bounds
are obtained for the orders of magnitude of the variances of the -th
intrinsic volumes of for . Furthermore,
strong laws of large numbers are proved for the intrinsic volumes of . The
essential tools are the Economic Cap Covering Theorem of B\'ar\'any and Larman,
and the Efron-Stein jackknife inequality
Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw
The intrinsic volumes of Gaussian polytopes are considered. A lower variance
bound for these quantities is proved, showing that, under suitable
normalization, the variances converge to strictly positive limits. The
implications of this missing piece of the jigsaw in the theory of Gaussian
polytopes are discussed
Finite Satisfiability for Guarded Fixpoint Logic
The finite satisfiability problem for guarded fixpoint logic is decidable and
complete for 2ExpTime (resp. ExpTime for formulas of bounded width)
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