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PoissonVoronoi Tesselation
, 2005
"... The ddimensional Poisson process of intensity λ is a random scattering of points (called particles) inR d that meets the following two requirements. Let S ⊆ R d denote a measurable set of finite volume μ and N(S) denote the number of particles falling in S. We have [1,2] • P {N(S) =n} = e −λμ (λμ) ..."
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The ddimensional Poisson process of intensity λ is a random scattering of points (called particles) inR d that meets the following two requirements. Let S ⊆ R d denote a measurable set of finite volume μ and N(S) denote the number of particles falling in S. We have [1,2] • P {N(S) =n} = e −λμ (λμ
The Proportion Of Triangles In A PoissonVoronoi Tessellation Of The Plane
, 1999
"... By using an adaptation of the radial generation method, we give an integral formula for the proportion of triangles in a PoissonVoronoi tessellation, which gives a value of 0.0112354 to 7 decimal places. We also obtain the first four moments of some characteristics of triangles. ..."
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Cited by 5 (0 self)
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By using an adaptation of the radial generation method, we give an integral formula for the proportion of triangles in a PoissonVoronoi tessellation, which gives a value of 0.0112354 to 7 decimal places. We also obtain the first four moments of some characteristics of triangles.
FRACTAL RANDOM SERIES GENERATED BY POISSONVORONOI TESSELLATIONS
, 2013
"... In this paper, w econstruct a new family of random series defined on R D, indexed by one scaling parameter and two Hurstlike exponents. The model is close to TakagiKnopp functions, save for the fact that the underlying partitions of R D are not the usual dyadic meshes but random Voronoi tessella ..."
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tessellations generated by Poisson point processes. This approach leads us to a continuous function whose random graph is shown to be fractal with explicit and equal box and Hausdorff dimensions. The proof of this main result is based on several new distributional properties of the PoissonVoronoi tessellation
Approximations of functionals of some modulatedPoisson Voronoi tessellations with applications to modeling of communication networks
"... apport de rechercheApproximations of functionals of some modulatedPoisson Voronoi tessellations with applications to modeling of communication networks ..."
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Cited by 2 (0 self)
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apport de rechercheApproximations of functionals of some modulatedPoisson Voronoi tessellations with applications to modeling of communication networks
Extreme values for characteristic radii of a PoissonVoronoi tessellation
, 2014
"... A homogeneous PoissonVoronoi tessellation of intensity γ is observed in a convex body W. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and included in the cell, and the circumscribed radius, i.e. the ..."
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Cited by 3 (1 self)
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A homogeneous PoissonVoronoi tessellation of intensity γ is observed in a convex body W. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and included in the cell, and the circumscribed radius, i
Anchored expansion, speed, and the hyperbolic Poisson Voronoi tessellation. ArXiv eprints
, 2014
"... Abstract. We show that random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random triangulations of the hyperbolic plane, the hyperbolic Poisson Voronoi tessellation and the hyperbolic Poisson D ..."
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Cited by 2 (0 self)
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Abstract. We show that random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random triangulations of the hyperbolic plane, the hyperbolic Poisson Voronoi tessellation and the hyperbolic Poisson
On a Coverage Process Ranging from the Boolean Model to the Poisson Voronoi Tessellation With Applications to Wireless Communications
 Adv. Appl. Prob
, 2001
"... We define and analyze a random coverage process of the ddimensional Euclidean space which allows one to describe a continuous spectrum that ranges from the Boolean model to the PoissonVoronoi tessellation to the JohnsonMehl model. Like for the Boolean model, the minimal stochastic setting consist ..."
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Cited by 58 (13 self)
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We define and analyze a random coverage process of the ddimensional Euclidean space which allows one to describe a continuous spectrum that ranges from the Boolean model to the PoissonVoronoi tessellation to the JohnsonMehl model. Like for the Boolean model, the minimal stochastic setting
Numerical And Analytical Computation Of Some SecondOrder Characteristics Of Spatial PoissonVoronoi Tessellations
, 1998
"... this paper we are concerned with Voronoi (or Dirichlet, or Thiessen) tessellations ..."
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Cited by 6 (3 self)
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this paper we are concerned with Voronoi (or Dirichlet, or Thiessen) tessellations
Statistical properties of planar Voronoi tessellations
, 2008
"... I present a concise review of advances realized over the past three years on planar PoissonVoronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data. ..."
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Cited by 2 (0 self)
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I present a concise review of advances realized over the past three years on planar PoissonVoronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data.
Results 1  10
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