# Coursebooks

## Lattice models

Hongler Clément

English

#### 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

We will discuss some classical lattice models, such as: random walks, percolation, Ising model, random spanning trees, gaussian free field.

We will prove non-trivial theorems for each of the models. The goal is to allow students to learn general methods and concepts from a number of detailed case studies.

#### Keywords

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

#### Learning Prerequisites

##### Required courses

Basic probability, basic analysis, linear algebra

I think that students who like to learn in the definition/theorem/proof/lemma way might be disappointed.

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

#### Assessment methods

Exam written

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

### In the programs

• Applied Mathematics, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Lattice models
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German