Lattice models

Summary

Lattice models consist of (typically random) objects living on a periodic graph. We will study some models that are mathematically interesting and representative of physical phenomena seen in the real world.

Content

Keywords

probability, graph theory, complex analysis, lattice models, statistical mechanics

Learning Prerequisites

Required courses

Basic probability, basic analysis, linear algebra

While the class will be completely rigorous, the emphasis is more on revealing some interesting phenomena (that somehow exists in nature) rather than on constructing some theories. The goal is to learn things that are generalizable, but I almost always prefer to work out particular cases first.

Recommended courses

None of this is mandatory, but it could help: complex analysis, basic graph theory, simulations

Learning Outcomes

• Reason with probabilistic lattice models
• Manipulate random variables in geometric settings
• Manipulate discrete and continuous objects

Assessment methods

Written exam

Dans le cas de l'€™art. 3 al. 5 du réglement de section, l'€™enseignant décide de la forme de l'€™examen qu'€™il communique aux étudiants concernés