On the distribution of overlaps in the Sherrington-Kirkpatrick spin glass model

This paper describes some of the analytic tools developed recently by Ghirl anda and Guerra in the investigation of the distribution of overlaps in the Sherrington-Kirkpatrick spin glass model and of Parisi's ultrametricity. I n particular, we introduce to this task a simplified (but also generalized) model on which the Gaussian analysis is made easier. Moments of the Hamilt onian and derivatives of the free energy are expressed as polynomials of th e overlaps. Under the essential tool of self-averaging, we describe with fu ll rigour, various overlap identities and replica independence that actuall y hold in a rather large generality. The results are presented in a languag e accessible to probabilists and analysts..