Every planar graph with the Liouville property is amenable. Issue 3 (7th June 2020)
- Record Type:
- Journal Article
- Title:
- Every planar graph with the Liouville property is amenable. Issue 3 (7th June 2020)
- Main Title:
- Every planar graph with the Liouville property is amenable
- Authors:
- Carmesin, Johannes
Georgakopoulos, Agelos - Abstract:
- Abstract : We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the existence of Dirichlet harmonic function s proved by Benjamini and Schramm. As a corollary we obtain that every planar nonamenable graph admits nonconstant Dirichlet harmonic function s27.
- Is Part Of:
- Random structures & algorithms. Volume 57:Issue 3(2020)
- Journal:
- Random structures & algorithms
- Issue:
- Volume 57:Issue 3(2020)
- Issue Display:
- Volume 57, Issue 3 (2020)
- Year:
- 2020
- Volume:
- 57
- Issue:
- 3
- Issue Sort Value:
- 2020-0057-0003-0000
- Page Start:
- 706
- Page End:
- 729
- Publication Date:
- 2020-06-07
- Subjects:
- circle packing -- electrical network -- harmonic function -- infinite graph -- non‐amenable -- planar graphs -- recurrent -- transient
Random graphs -- Periodicals
Mathematical analysis -- Periodicals
519 - Journal URLs:
- http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2418 ↗
http://onlinelibrary.wiley.com/ ↗ - DOI:
- 10.1002/rsa.20936 ↗
- Languages:
- English
- ISSNs:
- 1042-9832
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 7254.411950
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 13874.xml