A Central Limit Theorem for Convex Chains in the Square

被引：0

作者：

I. Bárány

G. Rote

W. Steiger

C.-H. Zhang

机构：

[1] Mathemetical Institute,

[2] Hungarian Academy of Sciences,undefined

[3] Pf. 127,undefined

[4] H-1364 Budapest,undefined

[5] Hungary barany@math-inst.hu ,undefined

[6] Institut für Mathematik,undefined

[7] Technische Universität Graz,undefined

[8] Steyrergasse 30,undefined

[9] A-8010 Graz,undefined

[10] Austria rote@opt.math.tu-graz.ac.at ,undefined

[11] Department of Computer Science,undefined

[12] Rutgers University,undefined

[13] Piscataway,undefined

[14] NJ 08903,undefined

[15] USA steiger@cs.rutgers.edu ,undefined

[16] Department of Statistics,undefined

[17] Rutgers University,undefined

[18] Piscataway,undefined

[19] NJ 08903,undefined

[20] USA cunhui@stat.rutgers.edu,undefined

来源：

Discrete & Computational Geometry | 2000年 / 23卷

关键词：

Direct Consequence; Limit Theorem; Central Limit; Central Limit Theorem; Weak Convergence;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Points P1,... ,Pn in the unit square define a convex n -chain if they are below y=x and, together with P0=(0,0) and Pn+1=(1,1) , they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature is that the limit shape is a direct consequence of the method. The main result is an accompanying central limit theorem for these chains. A weak convergence result implies several other statements concerning the deviations between random convex chains and their limit.

引用

页码：35 / 50

页数：15