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 $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{ 3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.
Categories: math.PR math-ph math.MP