The algebraic area of closed lattice random walks
Mathematical Physics
2019-09-04 v2 Combinatorics
math.MP
Abstract
We propose a formula for the enumeration of closed lattice random walks of length enclosing a given algebraic area. The information is contained in the Kreft coefficients which encode, in the commensurate case, the Hofstadter secular equation for a quantum particle hopping on a lattice coupled to a perpendicular magnetic field. The algebraic area enumeration is possible because it is split in pieces, each tractable in terms of explicit combinatorial expressions.
Keywords
Cite
@article{arxiv.1810.04098,
title = {The algebraic area of closed lattice random walks},
author = {Stephane Ouvry and Shuang Wu},
journal= {arXiv preprint arXiv:1810.04098},
year = {2019}
}
Comments
20 pages, 1 figure, misprints corrected, one section in the Appendix added