Metadata
Abstract
Typical weighted random simplices , , in a Poisson–Delaunay tessellation in are considered, where the weight is given by the st power of the volume. As special cases this includes the typical () and the usual volume-weighted () Poisson–Delaunay simplex. By proving sharp bounds on cumulants it is shown that the logarithmic volume of satisfies a central limit theorem in high dimensions, that is, as . In addition, rates of convergence are provided. In parallel, concentration inequalities as well as moderate deviations are studied. The set-up allows the weight to depend on the dimension as well. A number of special cases are discussed separately. For fixed also mod- convergence and the large deviations behaviour of the logarithmic volume of are investigated.
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