On non-uniqueness of percolation on nonamenable Cayley graphs *

By Igor Pak, Tatiana Smirnova-Nagnibeda. 2000

90 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a36a357e9904c9cb39fdf33126895d7dcee4ee64

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Damien Gaboriau
2. Russell Lyons
3. Yuval Peres
4. Wendelin Werner
5. Alexei Borodin
6. Ben Morris

In Mathematical Physics

1. Russell Lyons
2. Yuval Peres
3. Damien Gaboriau
4. Adrian Ioana
5. Y. Kida
6. Alexei Borodin
7. Pablo Shmerkin
8. Charles Bordenave

In Statistics and Probability

1. Russell Lyons
2. Damien Gaboriau
3. Yuval Peres
4. Alexei Borodin
5. Charles Bordenave
6. Manjunath Krishnapur
7. Pietro Caputo
8. Subhro Ghosh

Citations in the corpus

• Probability on Trees and Networks (2017, background): “This is known as Parrondo’s paradox, as it combines games that are not winning into a winning game. See Parrondo (1996) and Harmer and Abbott (1999).”
• Invariant percolation and harmonic Dirichlet functions (2004, background): “Smirnova-Nagnibeda [PSN00] proved that each finitely generated nonamenable group admits a Cayley graph for which pc < pu.”