Spatial Populations with Seed-Bank: Renormalisation on the Hierarchical Group

Andreas Greven, Universitat Erlangen-Nurnberg, Germany.Frank den Hollander, Universiteit Leiden, The Netherlands.Margriet Oomen, Universiteit Leiden, The Netherlands.

• Chapters1. Background, goals, and outline1. Model and Main Results2. Introduction of model and basic properties3. Main results: $N<\infty $, identification of clustering regime4. Main results: $N\to \infty $, renormalisation and multi-scale limit5. Main results $N\to \infty $: Orbit and cluster formation2. Preparations and Proofs6. Proofs: $N<\infty $, identification of clustering regime7. Preparation: $N\to \infty $, McKean-Vlasov process and mean-field8. Proofs: $N\to \infty $, mean-field finite-systems scheme9. Proofs: $N\to \infty $, mean-field, proof of abstract scheme10. Preparation: $N\to \infty $, two-colour mean-field11. Preparation: $N\to \infty $, two-level three-colour12. Proofs: $N\to \infty $, hierarchical multi-scale limit theorems13. Proofs: $N\to \infty $, orbit of renormalisation transformationA. Computation of scaling coefficientsB. Meyer-Zheng topology