The Martingale Method for Mean-Field Disordered Systems at High Temperature

We review some martingale techniques for the study of meanfield disordered systems at high temperature, including the Sherrington-Kirkpatrick model, the Hopfield model, and more general associative memory models. We describe the log-normal limit of the partition function in term of a Brownian motion, and we give another proof of self-averaging for pressure. In the Sherrington-Kirkpatrick case we show that the law of the product of two independent configurations is close to uniform at very high temperature, but this does not persist in the whole high-temperature region.