Area-width scaling in generalised Motzkin paths

Nils Haug, Thomas Prellberg and Grzegorz Siudem

Physica A: Statistical Mechanics and its Applications, 2017, vol. 482, issue C, 611-620

Abstract: We consider a generalised version of Motzkin paths, where horizontal steps have length ℓ, with ℓ being a fixed positive integer. We first give the general functional equation for the area-width generating function of this model. Using a heuristic ansatz, we then derive the area-width scaling behaviour in terms of a scaling function in one variable for the special cases of Dyck, (standard) Motzkin and Schröder paths, before generalising our approach to arbitrary ℓ. We then rigorously derive the tricritical scaling of Schröder paths by applying the generalised method of steepest descents to the known exact solution for their area-width generating function. Our results show that for Dyck and Schröder paths, the heuristic scaling ansatz reproduces the rigorous results.

Keywords: Exact solutions; Scaling functions; Basic hypergeometric series; Schroeder paths; Saddle point method; Dominant balance (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437117304612
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:482:y:2017:i:c:p:611-620

DOI: 10.1016/j.physa.2017.04.151

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 ().