RANDOM-WALKS IN NONINTEGER DIMENSION

被引:25
作者
BENDER, CM [1 ]
BOETTCHER, S [1 ]
MEAD, LR [1 ]
机构
[1] UNIV SO MISSISSIPPI,DEPT PHYS & ASTRON,HATTIESBURG,MS 39406
关键词
D O I
10.1063/1.530778
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
One can define a random walk on a hypercubic lattice in a space of integer dimension D. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given number of time steps. These formulas are physically meaningful for integer values of D. However, these formulas are unacceptable as probabilities when continued to noninteger D because they give values that can be greater than 1 or less than 0. In this paper a different kind of random walk is proposed which gives acceptable probabilities for all real values of D. This D-dimensional random walk is defined on a rotationally symmetric geometry consisting of concentric spheres. The exact result is given for the probability of returning to the origin for all values of D in terms of the Riemann zeta function. This result has a number-theoretic interpretation.
引用
收藏
页码:368 / 388
页数:21
相关论文
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