Random walks on hyperspheres of arbitrary dimensions

被引:18
作者
Caillol, JM [1 ]
机构
[1] Univ Paris 11, UMR 8267, Phys Theor Lab, F-91405 Orsay, France
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2004年 / 37卷 / 09期
关键词
D O I
10.1088/0305-4470/37/9/001
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider random walks on the surface of the sphere Sn-1 (n greater than or equal to 2) of the n-dimensional Euclidean space E-n, in short a hypersphere. By solving the diffusion equation-in Sn-1 we show that the usual law <r(2)> proportional to t valid in En-1 should be replaced in Sn-1 by the generic law <costheta> proportional to exp(-t/tau), where theta denotes the angular displacement of the walker. More generally one has <C-L(n/2-1)(cos theta)> proportional to exp(-t/tau(L,n)) where C-L(n/2-1) is a Gegenbauer polynomial. Conjectures concerning random walks on a fractal inscribed in Sn-1 are given tentatively.
引用
收藏
页码:3077 / 3083
页数:7
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