Ergodicity and the bootstrap percolation

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Table of contents

Remerciements
Abstract
Résumé
Chapter 1. Introduction
1.1. Glasses and the liquid-glass transition
1.2. Kinetically constrained models
1.3. Ergodicity and the bootstrap percolation
1.4. Time scales
1.5. Random environments
1.6. Overview of the results
1.7. List of conventions and notation
Chapter 2. Variational tools
2.1. Spectral gap and relaxation time
2.2. Hitting times
2.3. The time spent in E
Chapter 3. Random constraints on Zd
3.1. Introduction of the models
3.2. Bootstrap percolation on Z2 with threshold 1 or 2
3.3. Fredrickson-Andersen model on Z2 with threshold 1 or 2
3.4. Fredrickson-Andersen model on Zd with threshold 1 or d
3.5. Mixed North-East and Fredrickson-Andersen 1 spin facilitated models on Z2
3.6. Fredrickson-Andersen 1 spin facilitated model on the polluted Z2
3.7. Fredrickson-Andersen 2 spin facilitated model on polluted Z2
Chapter 4. Models on the Galton-Watson tree
4.1. Model, notation, and preliminary results
4.2. Metastability of the bootstrap percolation
4.3. Fredrickson-Andersen model on a Galton-Watson tree one example
Chapter 5. The Kob-Andersen model on Zd
5.1. The Kob-Andersen model and the main result
5.2. Proof of the main theorem
Chapter 6. Questions
6.1. KCMs and bootstrap percolation in random environments
6.2. The Kob-Andersen model
Bibliography