Peeling Random Planar Maps
Springer International Publishing (Verlag)
978-3-031-36853-0 (ISBN)
A "Markovian" approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface.
Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhD students and researchers interested in graph theory, combinatorial probability and geometry. Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps.lt;b>Nicolas Curien has been a Professor at Université Paris-Saclay since 2014. He works on random geometry in a broad sense.
- Part I (Planar) Maps. - 1. Discrete Random Surfaces in High Genus. - 2. Why Are Planar Maps Exceptional?. - 3. The Miraculous Enumeration of Bipartite Maps. - Part II Peeling Explorations. - 4. Peeling of Finite Boltzmann Maps. - 5. Classification of Weight Sequences. - Part III Infinite Boltzmann Maps. - 6. Infinite Boltzmann Maps of the Half-Plane. - 7. Infinite Boltzmann Maps of the Plane. - 8. Hyperbolic Random Maps. - 9. Simple Boundary, Yet a Bit More Complicated. - 10. Scaling Limit for the Peeling Process. - Part IV Percolation(s). - 11. Percolation Thresholds in the Half-Plane. - 12. More on Bond Percolation. - Part V Geometry. - 13. Metric Growths. - 14. A Taste of Scaling Limit. - Part VI Simple Random Walk. - 15. Recurrence, Transience, Liouville and Speed. - 16. Subdiffusivity and Pioneer Points.
"This lengthy monograph is an excellent addition to the long-running École d'Été de Probabilités de Saint-Flour series of extended lecture notes, continuing their tradition of reader-friendly (for an active researcher in mathematical probability) authoritative accounts of an active technical topic. It has the traditional underlying definition/ theorem/proof format ... and numerous well thought out figures, which (to your reviewer) are essential for any work on graph theory. ... this monograph will long remain a key account of its topics." (David J. Aldous, Mathematical Reviews, December, 2024)
| Erscheinungsdatum | 22.11.2023 |
|---|---|
| Reihe/Serie | École d'Été de Probabilités de Saint-Flour | Lecture Notes in Mathematics |
| Zusatzinfo | XVIII, 286 p. 120 illus., 98 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 468 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | Coding Processes of Random Trees • Combinatorial Geometry • Combinatorial probability • combinatorics • graph theory • Markov Property • Peeling Exploration in the Random Planar Map • Planar Maps • Random Geometry • scaling limits • stable processes |
| ISBN-10 | 3-031-36853-3 / 3031368533 |
| ISBN-13 | 978-3-031-36853-0 / 9783031368530 |
| Zustand | Neuware |
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