In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1 i ... σs i. 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.
@article{urn:eudml:doc:41891,
title = {On the multiple overlap function of the SK model. },
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {163-199},
mrnumber = {MR2307151},
zbl = {1207.82027},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41891}
}
Bezerra, Sergio de Carvalho; Tindel, Samy. On the multiple overlap function of the SK model. . Publicacions Matemàtiques, (2007), pp. 163-199. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41891/