Random geometric subdivisions

被引：2
|
作者：
Volkov, Stanislav [1 ,2 ]
机构：
[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
[2] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden
来源：
RANDOM STRUCTURES & ALGORITHMS | 2013年 / 43卷 / 01期
关键词：
barycentric subdivision; geometric probability; Markov chain; iterated random functions;
D O I：
10.1002/rsa.20454
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We study several models of random geometric subdivisions arising from the model of Diaconis and Miclo (Combin Probab Comput 20 (2011) 213-237). In particular, we show that the limiting shape of an indefinite subdivision of a quadrilateral is a.s. a parallelogram. We also show that the geometric subdivisions of a triangle by angle bisectors converge (only weakly) to a non-atomic distribution, and that the geometric subdivisions of a triangle by choosing random points on its sides converges to a flat triangle, similarly to the result of Diaconis and Miclo (Combin Probab Comput 20 (2011) 213-237). (c) 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013
引用
收藏
页码：115 / 130
页数：16
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