Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 4 (2012), 938-953.
Set reconstruction by Voronoi cells
For a Borel set A and a homogeneous Poisson point process η in ∝d of intensity λ>0, define the Poisson--Voronoi approximation Aη of A as a union of all Voronoi cells with nuclei from η lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AΔ Aη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AΔ Aη) together with their asymptotics for large λ are obtained as well.
Adv. in Appl. Probab., Volume 44, Number 4 (2012), 938-953.
First available in Project Euclid: 5 December 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 60C05: Combinatorial probability
Reitzner, M.; Spodarev, E.; Zaporozhets, D. Set reconstruction by Voronoi cells. Adv. in Appl. Probab. 44 (2012), no. 4, 938--953. doi:10.1239/aap/1354716584. https://projecteuclid.org/euclid.aap/1354716584