Sergio Caracciolo, Andrea Sportiello
The height probabilities for the recurrent configurations in the Abelian Sandpile Model on the square lattice have analytic expressions, in terms of multidimensional quadratures, which have been determined numerically with high accuracy, and conjectured to be certain cubic rational-coefficient polynomials in 1/pi. We complete the exact determination of these probabilities, by computing analytically the corresponding integrals. We confirm the predictions on the probabilities, and thus, as a corollary, the conjecture on the average height.
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http://arxiv.org/abs/1207.6074
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