Asymptotic approximation of smooth convex bodies by polytopes.
Asymptotic mean values of Gaussian polytopes.
Asymptotics of variance of the lattice point count
The variance of the number of lattice points inside the dilated bounded set with random position in has asymptotics if the rotational average of the squared modulus of the Fourier transform of the set is . The asymptotics follow from Wiener’s Tauberian theorem.
Bernoulli cluster field: Voronoi tessellations
A new point process is proposed which can be viewed either as a Boolean cluster model with two cluster modes or as a -thinned Neyman-Scott cluster process with the retention of the original parent point. Voronoi tessellation generated by such a point process has extremely high coefficients of variation of cell volumes as well as of profile areas and lengths in the planar and line induced tessellations. An approximate numerical model of tessellation characteristics is developed for the case of small...
Berry-Esseen bounds for projections of coordinate symmetric random vectors.
Berry-Esseen bounds for the number of maxima in planar regions.
Boolean cluster models: mean cluster dilations and spherical contact distances
Boolean cluster point processes with various cluster distributions are examined by means of their spherical contact distribution function. Special attention is paid to clusters with strong independence properties (Poisson clusters) and regular clusters.
Central limit theorem for Gibbsian U-statistics of facet processes
A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction U-statistics are calculated and the central limit theorem is derived using the method of moments.
Central limit theorem for random measures generated by stationary processes of compact sets
Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.
Coarsening, nucleation, and the marked brownian web
Compact convex sets of the plane and probability theory
The Gauss−Minkowski correspondence in ℝ2 states the existence of a homeomorphism between the probability measures μ on [0,2π] such that ∫ 0 2 π e ix d μ ( x ) = 0 and the compact convex sets (CCS) of the plane with perimeter 1. In this article, we bring out explicit formulas relating the border of a CCS to its probability measure. As a consequence, we show that some natural operations on CCS – for example, the Minkowski sum – have natural translations in terms of probability measure operations,...
Complex determinantal processes and noise.
Comportement asymptotique des fonctions harmoniques en courbure négative.
Concentration of measure and isoperimetric inequalities in product spaces
Concept of Data Depth and Its Applications
Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem.
Confirmation of Matheron's conjecture on the covariogram of a planar convex body
Conformal restriction and related questions.
Connected allocation to Poisson points in .
Connexions et martingales dans les groupes de Lie
Convergence of coalescing nonsimple random walks to the Brownian web.