Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Critical Percolation on any Nonamenable Group Has no Infinite Clusters

Itai Benjamini, Russell Lyons, Yuval Peres and Oded Schramm
The Annals of Probability
Vol. 27, No. 3 (Jul., 1999), pp. 1347-1356
Stable URL: http://www.jstor.org/stable/2652805
Page Count: 10
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Critical Percolation on any Nonamenable Group Has no Infinite Clusters
Preview not available

Abstract

We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter. This result was obtained by the present authors earlier as a corollary of a general study of group-invariant percolation. The goal here is to present a simpler self-contained proof that easily extends to quasi-transitive graphs with a unimodular automorphism group. The key tool is a "mass-transport" method, which is a technique of averaging in nonamenable settings.

Page Thumbnails

  • Thumbnail: Page 
1347
    1347
  • Thumbnail: Page 
1348
    1348
  • Thumbnail: Page 
1349
    1349
  • Thumbnail: Page 
1350
    1350
  • Thumbnail: Page 
1351
    1351
  • Thumbnail: Page 
1352
    1352
  • Thumbnail: Page 
1353
    1353
  • Thumbnail: Page 
1354
    1354
  • Thumbnail: Page 
1355
    1355
  • Thumbnail: Page 
1356
    1356