Introduction to Replica Theory

Abstract:  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 some 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 details. 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 in information theory and computer science
will be briefly discussed.

Hamed Hassani, Department of Electrical and Systems Engineering,
Department of Computer and Information Systems, University of
Pennsylvania