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Full Description
The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Contents
Chapters
1. Background, goals, and outline
1. Model and Main Results
2. Introduction of model and basic properties
3. Main results: $N<
\infty $, identification of clustering regime
4. Main results: $N\to \infty $, renormalisation and multi-scale limit
5. Main results $N\to \infty $: Orbit and cluster formation
2. Preparations and Proofs
6. Proofs: $N<
\infty $, identification of clustering regime
7. Preparation: $N\to \infty $, McKean-Vlasov process and mean-field
8. Proofs: $N\to \infty $, mean-field finite-systems scheme
9. Proofs: $N\to \infty $, mean-field, proof of abstract scheme
10. Preparation: $N\to \infty $, two-colour mean-field
11. Preparation: $N\to \infty $, two-level three-colour
12. Proofs: $N\to \infty $, hierarchical multi-scale limit theorems
13. Proofs: $N\to \infty $, orbit of renormalisation transformation
A. Computation of scaling coefficients
B. Meyer-Zheng topology
