  We consider ferromagnetic spin models on dilute random graphs and prove that,
with suitable one-body infinitesimal perturbations added to the Hamiltonian,
the multi-overlaps concentrate for all temperatures, both with respect to the
thermal Gibbs average and the quenched randomness. Results of this nature have
been known only for the lowest order overlaps, at high temperature or on the
Nishimori line. Here we treat all multi-overlaps by a non-trivial application
of Griffiths-Kelly-Sherman correlation inequalities. Our results apply in
particular to the pure and mixed p-spin ferromagnets on random dilute
Erdoes-R\'enyi hypergraphs. On physical grounds one expects that multi-overlap
concentration directly implies the correctness of the cavity (or replica
symmetric) formula for the pressure. The proof of this formula for the general
p-spin ferromagnet on a random dilute hypergraph remains an open problem.
