70th birthday of Vratislav Horálek
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...
Co neučíme, a měli bychom (a co učíme, ač bychom možná nemuseli)
What we do not teach and we should (and what we teach though maybe we should not)
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.
The life and work of Zbyněk Šidák (1933–1999)
Zbyněk Šidák, the chief editor of the Applications of Mathematics, an outstanding Czech statistician and probabilist, died on November 12, 1999, aged 66 years. This article is devoted to memory of him and outlines his life and scientific work.
Convergence of randomly oscillating point patterns to the Poisson point process
Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical...
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