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401-5003-72L 2 Credits DR D-MATH

A PDE Approach to Mean-Field Disordered Systems

Lecturers & Examiners: Dr. Jean-Christophe Mourrat
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-02-05 16:02:04

Abstract

Nachdiplom lecture

Content

The goal of statistical mechanics is to describe the large-scale behavior of collections of simple elements, often called spins, that interact through locally simple rules and are influenced by some amount of noise. We will discuss three classes of such models, of increasing difficulty, and will rely on a common PDE approach to study each of them. The first model we will study is the very simple Curie-Weiss model, in which every spin interacts with every other spin and has a preference for being aligned with the others. This model can be solved in a variety of ways, but will be used to develop our toolkit based on the study of certain Hamilton-Jacobi equations that naturally arise. We will then turn to a more challenging class of models coming from statistical inference. We will focus on a setup in which we observe a noisy version of a large rank-one matrix. We will compute the information-theoretic limit to the recovery of this matrix based on the PDE techniques introduced earlier. We will finally discuss spin-glass models, in which the local interactions between the spins are disordered. One of the core motivations for the development of the techniques presented here is to uncover the behavior of models in which spins can be of different types, such as for instance when the spins are organized over two layers, and only have direct interactions across layers. While the understanding of this class of models is still very limited, I will present some progress towards this goal.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture A PDE Approach to Mean-Field Disordered Systems
If you would like to attend the lecture please register by 30 September. For the registration form see
  • Wed 10:15-12:00 (HG G 43)
24 h semesterly

Offered In