Coarse geometry and randomness
These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. T...
Salvato in:
| Ente Autore: | |
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| Altri autori: | |
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Cham :
Springer International Publishing
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2013. |
| Serie: | Lecture notes in mathematics
2100 École d'Été de Probabilités de Saint-Flour 41 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 133 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Coarse geometry and randomness, École d'Été de Probabilités de Saint-Flour XLI - 2011, 2013, Cham (Suisse) [etc.], Springer, 1 vol. (VII-129 p.), Lecture notes in mathematics, 978-3-319-02575-9 |
Sommario:
- Isoperimetry and expansions in graphs
- Several metric notions
- The hyperbolic plane and hyperbolic graphs
- More on the structure of vertex transitive graphs
- Percolation on graphs
- Local limits of graphs
- Random planar geometry
- Growth and isoperimetric profile of planar graphs
- Critical percolation on non-amenable groups
- Uniqueness of the infinite percolation cluster
- Percolation perturbations
- Percolation on expanders
- Harmonic functions on graphs
- Nonamenable Liouville graphs