Area versus Length Distribution for Closed Random Walks
arXiv:cond-mat/0212564 · doi:10.1088/0305-4470/36/6/301
Abstract
Using a connection between the -oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area, on a hypercubic lattice, in the limit of infinite number of dimensions. The formula is investigated in detail, and asymptotic behaviours are evaluated. The area distribution in the limit of long loops is computed. As a byproduct, we obtain also an infinite set of new, nontrivial identities.
17 pages
References in corpus (9)
- -Gaussian processes: non-commutative and classical aspects
- Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
- -dimensional Arrays of Josephson Junctions, Spin Glasses and -deformed Harmonic Oscillators
- Analysis of negative magnetoresistance. Statistics of closed paths. I. Theory
- Exact Random Walk Distributions using Noncommutative Geometry
- Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz
- Replica Theory and Large D Josephson Junction Hypercubic Models
- Solving the Frustrated Spherical Model with q-Polynomials
- Bandwidths Statistics from the Eigenvalue Moments for Harper-Hofstadter Problem