|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Random Walks on Hyperspheres of Arbitrary Dimensions | | Jean-Michel Caillol
; | | Date: |
13 Dec 2003 | | Journal: | J. Phys. A: Math. Gen. 37, 3077 (2004). | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | We consider random walks on the surface of the sphere $S_{n-1}$ ($n geq 2$) of the $n$-dimensional Euclidean space $E_n$, in short a hypersphere. By solving the diffusion equation in $S_{n-1}$ we show that the usual law $ varpropto t $ valid in $E_{n-1}$ should be replaced in $S_{n-1}$ by the generic law $ varpropto exp(-t/ au)$, where $ heta$ denotes the angular displacement of the walker. More generally one has $ varpropto exp(-t/ au(L,n))$ where $C^{n/2-1}_{L}$ a Gegenbauer polynomial. Conjectures concerning random walks on a fractal inscribed in $S_{n-1}$ are given tentatively. | | Source: | arXiv, cond-mat/0401209 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER