The gelation phase transition

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Table of contents

1 Introduction 
1 Content of the thesis
2 A short history of Smoluchowski’s equation
3 Smoluchowski’s equation of limited aggregations
4 A two-type limited aggregation model
5 Post-gelation uniqueness of coagulation equations
6 A microscopic model for Smoluchowski’s equation
2 A model for coagulation with mating 
1 Introduction
2 Setting and results
3 Preliminary results
4 Proof of the theorem
5 Explicit formulas
6 Limiting concentrations and Galton-Watson processes
7 Microscopic model
3 Post-gelation uniqueness of coagulation equations 
1 Introduction
2 Smoluchowski’s equation
3 Flory’s equation
4 The model with limited aggregations
5 The modified version
6 Limiting concentrations
4 SOC in a microscopic model for Smoluchowski’s equation 
1 Introduction
2 Presentation of the model and of the results
3 Convergence to Smoluchowski’s equation
4 Pre-gelation results
5 Preliminary results
6 Subcriticality
7 Tightness
8 Self-organized criticality
9 Asymptotic independence
10 Evolution in time
A Exploration process of a configuration model
B Tightness
C Mass in Smoluchowski’s and Flory’s models
D Exploration process of a two-type uniform pairing
Bibliography

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