Interacting particles on graphs

For more info about our services contact : help@bestpfe.com

Table of contents

Remerciements
Abstract
Résumé
Chapter 1. Introduction
1. Weakly interacting particle systems
2. Graph sequences and graphons
3. Interacting particles on graphs
4. Motivations
5. Overview of the results and general organization
Chapter 2. Interacting diusions on Erd®s-Rényi random graphs
1. Introduction
2. Main results
3. Proof: The Law of Large Numbers
4. Proof: Large Deviation Principle
Chapter 3. Weakly interacting oscillators on dense random graphs
1. Introduction, organization and set-up
2. The models and main results
3. The non-linear process
4. Proof of Theorem 2.3
3.A. Graph convergence and random graphons
Chapter 4. Long time dynamics for interacting oscillators
1. Introduction
2. Main results
3. Longtime dynamics close to M
4. Longtime behavior around 1=2
5. Finite time behavior
4.A. Graphs
4.B. H􀀀1 and Semigroups
Chapter 5. A Law of Large Numbers via a mild formulation
1. Introduction
2. Main result
3. Proofs
5.A. Hilbert spaces and semigroups
5.B. Rough integration associated to semigroup functionals
Chapter 6. Perspectives
1. From dense graph sequences to the sparse regime
2. Irregular graphons and random graphons
3. Unbounded graphons
4. Long-time dynamics and uniform propagation of chaos
Bibliography