Random Walks on Hyperspheres of Arbitrary Dimensions

Details Random Walks on Hyperspheres of Arbitrary Dimensions Random Walks on Hyperspheres of Arbitrary Dimensions

2004-01-13

arxiv.org/abs/cond-mat/0401209v1

J. Phys. A: Math. Gen. 37, 3077 (2004).

Physics

Condensed Matter

Statistical Mechanics

10 pages

Scientific paper

10.1088/0305-4470/37/9/001

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 $<\cos \theta > \varpropto \exp(-t/\tau)$, where $\theta$ denotes the angular displacement of the walker. More generally one has $ \varpropto \exp(-t/ \tau(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.

Affiliated with

Also associated with

No associations

Rating

Random Walks on Hyperspheres of Arbitrary Dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Walks on Hyperspheres of Arbitrary Dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Walks on Hyperspheres of Arbitrary Dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-266377