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arXiv · 1810.04098

The algebraic area of closed lattice random walks

Stephane Ouvry·Shuang Wu
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Abstract

We propose a formula for the enumeration of closed lattice random walks of length $n$ 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 $2^{n/2-1}$ pieces, each tractable in terms of explicit combinatorial expressions.

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Stephane Ouvry, Shuang Wu. 2018-10-09. The algebraic area of closed lattice random walks. https://doi.org/10.1088/1751-8121/ab2107

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