STAIRCASE POLYGONS AND RECURRENT LATTICE WALKS

Authors
GLASSER ML MONTALDI E
Citation
Ml. Glasser et E. Montaldi, STAIRCASE POLYGONS AND RECURRENT LATTICE WALKS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(4), 1993, pp. 180002339-180002342
Citations number
5
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
48
Issue
4
Year of publication
1993
Pages
180002339 - 180002342
Database
ISI
SICI code
1063-651X(1993)48:4<180002339:SPARLW>2.0.ZU;2-1
Abstract
In this paper we derive a direct relationship between the staircase-po lygon-generating function Z(d) Of Guttmann and Prellberg [Phys. Rev. E 47, R2233 (1993)] and the generating function for recurrent lattice w alks P(d) for the simple (hyper-) cubic lattice in all dimensions d. A recursion formula is obtained for the Z(d) with respect to dimension, which leads to a simplified derivation of Guttmann and Prellberg's re sult for d = 3, avoiding the use of the Heun function, and a derivatio n of their formula for d = 4 from an integral representation is given in the Appendix.