401-5003-72L  A PDE Approach to Mean-Field Disordered Systems

SemesterHerbstsemester 2022
DozierendeJ.‑C. Mourrat
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch
KommentarOnly 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 (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“.



Lehrveranstaltungen

NummerTitelUmfangDozierende
401-5003-72 VA 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 Link
24s Std.
Mi10:15-12:00HG G 43 »
J.‑C. Mourrat

Katalogdaten

KurzbeschreibungNachdiplom lecture
Lernziel
InhaltThe 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.
Voraussetzungen / BesonderesThe prerequisites for these lectures are basic measure theory and
probability theory. No prior knowledge of PDE theory will be assumed.

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte2 KP
PrüfendeJ.-C. Mourrat
Formunbenotete Semesterleistung
PrüfungsspracheEnglisch
RepetitionRepetition nur nach erneuter Belegung der Lerneinheit möglich.

Lernmaterialien

Keine öffentlichen Lernmaterialien verfügbar.
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

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Einschränkungen

VorrangDie Belegung der Lerneinheit ist nur durch die primäre Zielgruppe möglich
Primäre ZielgruppeDoktorat Mathematik (439002)
Doktorat Rechnergestützte Wissenschaften (439102)

Angeboten in

StudiengangBereichTyp
Doktorat MathematikGraduate SchoolWInformation