کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527361 | 958839 | 2014 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A general study of extremes of stationary tessellations with examples
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
Let m be a random tessellation in Rd, dâ¥1, observed in a bounded Borel subset W and f(â
) be a measurable function defined on the set of convex bodies. A point z(C), called the nucleus of C, is associated with each cell C of m. Applying f(â
) to all the cells of m, we investigate the order statistics of f(C) over all cells Câm with nucleus in WÏ=Ï1/dW when Ï goes to infinity. Under a strong mixing property and a local condition on m and f(â
), we show a general theorem which reduces the study of the order statistics to the random variable f(C), where C is the typical cell of m. The proof is deduced from a Poisson approximation on a dependency graph via the Chen-Stein method. We obtain that the point process {(Ïâ1/dz(C),aÏâ1(f(C)âbÏ)),Câm,z(C)âWÏ}, where aÏ>0 and bÏ are two suitable functions depending on Ï, converges to a non-homogeneous Poisson point process. Several applications of the general theorem are derived in the particular setting of Poisson-Voronoi and Poisson-Delaunay tessellations and for different functions f(â
) such as the inradius, the circumradius, the area, the volume of the Voronoi flower and the distance to the farthest neighbor.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 124, Issue 9, September 2014, Pages 2917-2953
Journal: Stochastic Processes and their Applications - Volume 124, Issue 9, September 2014, Pages 2917-2953
نویسندگان
Nicolas Chenavier,