Kinetically constrained models

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Table of contents

Introduction
1 Definitions and tools
1.1 Definitions
1.2 Bootstrap percolation
1.3 Relaxation time
2 Universality
2.1 Previous results
2.2 Advances of the thesis and universality partition
2.3 Sketch of proofs
3 Convergence to equilibrium
3.1 Previous results
3.2 Advances of the thesis
3.3 Sketch of proofs
1 Combinatorics for supercritical rooted kinetically constrained models
1.1 Introduction
1.2 Notations and result
1.3 The one-dimensional case
1.4 The general case
1.5 Sketch of the proof of proposition 1.6
2 Asymptotics for Duarte and supercritical rooted kinetically constrained models
2.1 Introduction
2.2 Models and notation
2.2.1 Notation
2.2.2 Models
2.3 A variational lower bound for E(0)
2.4 Supercritical rooted KCMs
2.5 The Duarte KCM
2.5.1 Preliminary tools: the Duarte bootstrap process
2.5.2 Algorithmic construction of the test function and proof of theorem 2.11
2.5.3 East-like motion of the arrows and proof of proposition
2.5.4 Density of droplets and proof of proposition 2.27
2.5.5 Finishing the proof of proposition 2.27
3 Asymptotics for critical kinetically constrained models with an infinite number of stable directions
3.1 Introduction
3.2 Models and background
3.2.1 Bootstrap percolation
3.2.2 Kinetically constrained models
3.2.3 Result
3.3 Sketch of the proof
3.4 Preliminaries and notation
3.5 Droplet algorithm
3.5.1 Clusters and crumbs
3.5.2 Distorted Young diagrams
3.5.3 Span
3.5.4 Droplet algorithm and spanned droplets
3.5.5 Properties of the algorithm
3.6 Renormalised East dynamics
3.6.1 Geometric setup
3.6.2 Arrow variables
3.6.3 Renormalised East dynamics
3.6.4 Proof of theorem 3.8
3.7 Open problems
4 Convergence to equilibrium in supercritical kinetically constrained models
4.1 Introduction
4.2 Notations and result
4.3 Dual paths
4.4 Codings
4.5 An auxiliary process
4.5.1 Local spread of zeroes
4.5.2 Definition of the auxiliary process
4.5.3 Properties of the auxiliary process
4.6 Proof of proposition 4.11
5 Convergence to equilibrium in the d-dimensional East model
5.1 Introduction
5.2 Notations and results
5.3 Proof of theorem 5.2
5.3.1 Finding a site that stays at zero for a time (t)
5.3.2 Proving the origin stays at zero for a time (t)
5.3.3 Ending the proof of theorem 5.2
5.4 Proof of corollary 5.4