The Sherrington-Kirkpatrick model: an overview

Abstract: The goal of this paper is to review some of the main ideas that emerged from the attempts to confirm mathematically the predictions of the celebrated Parisi ansatz in the Sherrington-Kirkpatrick model. We try to focus on the big picture while sketching the proofs of only a few selected results, but an interested reader can find most of the missing details in [31] and [44].