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arXiv · 1606.03273

On the algebraic area of lattice walks and the Hofstadter model

Stephane Ouvry·Stephan Wagner·Shuang Wu
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Abstract

We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of the Hofstadter Hamiltonian in terms of a complete elliptic integral, evaluated at a rational function. This in turn gives us both exact and asymptotic formulas for these moments.

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Stephane Ouvry, Stephan Wagner, Shuang Wu. 2016-06-10. On the algebraic area of lattice walks and the Hofstadter model. https://doi.org/10.1088/1751-8113%2F49%2F49%2F495205

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