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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...
This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/∞ queue. They describe in particular the
exponential dissipation of Φ-entropies along this process. This simple
queueing process appears as a model of “constant curvature”, and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
...
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.
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
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