On the multiple overlap function of the SK model.
In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R of the SK model, defined for given N, s ≥ 1 by R = NΣ σ ... σ . These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.