English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We are studying the motion of a random walker in generalized d dimensionalcontinuum with unit step length (up to 10 dimensions) and its projected onedimensional motion numerically. The motion of a random walker in lattice orcontinuum is well studied in statistical physics but what will be thestatistics of projected one dimensional motion of higher dimensional randomwalker is yet to be explored. Here in this paper, addressing this particulartype of problem, we have showed that the projected motion is diffusiveirrespective of any dimension, however, the diffusion rate is changinginversely with dimension. As a consequence, we can say that at infinitedimension the diffusion rate becomes zero. This is an interesting result, atleast pedagogically, which implies that though in infinite dimension there is adiffusion but its one dimensional projection is motionless. At the end of thediscussion we are able to make a good comparison between projected onedimensional motion of generalized d-dimensional random walk with unit steplength and pure one dimensional random walk with random step length varyinguniformly between -h to h where h is a step length renormalizing factor.

Statistics of Projected Motion in one dimension of a d-dimensional Random Walker