Published 2018
| Submitted
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Counterexamples for percolation on unimodular random graphs
- Creators
-
Angel, Omer
-
Hutchcroft, Tom
- Other:
-
Sobieczky, Florian
Chicago
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Abstract
We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with p_c = p_u for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with p_c < 1 but with an infinite cluster at criticality. These examples show that two well-known conjectures of Benjamini and Schramm are false when generalised from transitive graphs to unimodular random rooted graphs.
Additional Information
© 2018 Omer Angel and Thomas Hutchcroft. This was was carried out while TH was a PhD student at the University of British Columbia, during which time he was supported by a Microsoft Research PhD Fellowship.Attached Files
Submitted - 1710.03003.pdf
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Additional details
- Eprint ID
- 111008
- Resolver ID
- CaltechAUTHORS:20210922-193309642
- Microsoft Research
- Created
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2021-09-27Created from EPrint's datestamp field
- Updated
-
2021-09-27Created from EPrint's last_modified field
- Series Name
- Contemporary Mathematics
- Series Volume or Issue Number
- 719