Shapes and sizes of arbitrary random walks at O(1/d3) I. Most probable size ratio

Gaoyuan Wei

Physica A: Statistical Mechanics and its Applications, 1997, vol. 237, issue 3, 413-422

Abstract: For arbitrary random walks in any d-dimensional space, a 1/d expansion of the most probable size ratio, i.e., squared radius of gyration s2 divided by 〈s2〉 of open random walks, has been developed, which, at O(1/d3), yields a very good approximation to the exact value for chains (d ⩾ 2) and rings (d ⩾ 1), and for the first time, gives an estimate of the most probable size ratio for end-looped random walks. Asymptotic distribution functions for large and small size ratio have also been investigated analytically for open and closed random walks with explicit results given up to the fourth order for any values of d. For random walks at d = ∞, it has been proved that the most probable size coincides with mean size and the αth shape factor is inversely proportional to the αth eigenvalue of the architecture matrix for the walks.

Keywords: Random walks; Shapes and sizes; Polymer configuration statistics; Distribution function; Macromolecules (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843719600372X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:237:y:1997:i:3:p:413-422

DOI: 10.1016/S0378-4371(96)00372-X

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().