Coarse geometry and randomness : École d'Été de Probabilités de Saint-Flour XLI - 2011 /
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...
Saved in:
| Main Author: | |
|---|---|
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing Imprint: Springer,
2013.
|
| Series: | Lecture Notes in Mathematics,
2100 |
| Subjects: | |
| Online Access: | Click here to view the full text content |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.