On the size distribution of Poisson Voronoi cells
نویسندگان
چکیده
منابع مشابه
Large Poisson-Voronoi Cells and Crofton Cells
It is proved that the shape of the typical cell of a stationary Poisson-Voronoi tessellation in Euclidean space, under the condition that the volume of the typical cell is large, must be close to spherical shape, with high probability. The same holds if the volume is replaced by the surface area or other suitable functionals. Similar results hold for the zero cell of a stationary and isotropic ...
متن کاملDomain-size distribution in a Poisson-Voronoi nucleation and growth transformation.
We present an analytical result for the evolution of the domain-size distribution during the growth of simultaneously nucleated domains. The final stage of this transformation is the well-known Poisson-Voronoi tessellation. The method can be easily extended to the calculation of the probability distribution of any other geometric characteristic. As far as we know, it is the first time that an e...
متن کاملPoisson – Voronoi Approximation
Let X be a Poisson point process and K ⊂ R d a measurable set. Construct the Voronoi cells of all points x ∈ X with respect to X, and denote by vX (K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V (vX (K)) − V (K) and the symmetric difference V (vX (K)△K) is computed. Precise estimates for the variance of both quantities ...
متن کاملPoisson-Voronoi Tessellations
In particular, the location of S in R d is immaterial (stationarity) and E(N(S)) = λμ =Var(N(S)) (equality of mean and variance). An alternative characterization of the Poisson process involves the limit of the uniform distribution on expanding cubes C ⊆ R . Let ν denote the volume of C. Given m independent uniformly distributed particles in C and a measurable set S ⊆ C of volume μ, the probabi...
متن کاملSimulation of the typical Poisson - Voronoi - Cox - Voronoi cell
We consider stationary Poisson-Voronoi tessellations (PVT) in the Euclidean plane and study properties of Voronoi tessellations induced by linear Poisson processes on the edges of the PVT. We are especially interested in simulation algorithms for the typical cell. Two different simulation algorithms are introduced. The first algorithm directly simulates the typical cell whereas the second algor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2007
ISSN: 0378-4371
DOI: 10.1016/j.physa.2007.07.063