Short course

Hamed Hassani
Introduction to Replica Theory

The main goal of this short course is to provide an introductory overview of the replica method and its ramifications. the replica method is an amazing construction used to predict the outcome of somre complex computational procedures in statistical physics. it is not yet a rigorous method as it involves some formal manipulations, and a few predictions which may appear arbitrary. nevertheless, some of its important predictions have been confirmed rigorously using other approaches. we will introduce the replica method via the so-called random energy model which is a simple model that captures the essential detailes. we will also consider a more complicated spin model, called the fully connected spin glass model, and work out the predictions of the replica method. if time permits, some other applications theory in information theory and computer science will be briefly discussed.