The Curie-Weiss Model of SOC in Higher Dimension

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We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum Sₙ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order n³/⁴ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.