École Nationale Supérieure de
Techniques Avancées

Abstract

The purpose of this internship is to show that there is no overlap gap in the Parisi measure. First, we will describe the SK model so, we can understand the stakes of the problem (section 2). Then we will present a new variational representation of the Parisi functional (section 3). And we will find some conditions that the Parisi measure must respect (section 4). We will also present the link between the new representation and the other one (section 5). In this report, we will present a few of the unsuccessful paths we have explored (section 7) . At the end, you'll see that we have brought a new representation which is strongly linked to the usual one. We haven't managed to solve the problem (section 6). But we hope that we have found useful tools that will help other to find out a solution to the problem.