|
|||||
|
|
Nonamenable products are not treeable |
|
| Authors: | Robin Pemantle Yuval Peres |
| Institution: | (1) Department of Mathematics, University of Wisconsin, 53706 Madison, WI, USA;(2) Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel;(3) Department of Statistics, University of California, 94720 Berkeley, CA, USA |
| Abstract: | LetX andY be infinite graphs such that the automorphism group ofX is nonamenable and the automorphism group ofY has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct productX×Y. This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product has infinitely many connected components almost surely. Research partially supported by NSF grant DMS-9803597. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |