Marginals of a spherical spin glass model with correlated disorder

In this paper we prove the weak convergence, in high-temperature phase, of finite marginals Gibbs measure associated to a symmetric spherical spin glass model with correlated couplings towards an explicit asymptotic decoupled measure. We also provide upper bounds for rate convergence terms one energy per variable. Furthermore, establish concentration inequality bounded functions subset phase. These results are exemplified by analysing behaviour empirical mean coordinate-wise samples from model.