Some Conditional Correlation Inequalities for Percolation and Related Processes
| dc.creator | Berg, Jacob van den | |
| dc.creator | Haggstrom, Olle | |
| dc.creator | Kahn, Jeff | |
| dc.date | 2004-08-13 | |
| dc.date.accessioned | 2026-07-07T05:11:15Z | |
| dc.date.available | 2026-07-07T05:11:15Z | |
| dc.description | Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive) result that, conditioned on the event that there is no open path from s to t, the two events "there is an open path from s to a" and "there is an open path from s to b" are positively correlated. In the present paper we further investigate and generalize the theorem of which this result was a consequence. This leads to results saying, informally, that, with the above conditioning, the open cluster of s is conditionally positively (self-)associated and that it is conditionally negatively correlated with the open cluster of t. We also present analogues of some of our results for (a) random-cluster measures, and (b) directed percolation and contact processes, and observe that the latter lead to improvements of some of the results in a paper of Belitsky, Ferrari, Konno and Liggett (1997). | |
| dc.identifier | https://arxiv.org/abs/math/0408176 | |
| dc.identifier | http://arxiv.org/abs/math/0408176 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72179 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05; 60K35; 05C99 | |
| dc.title | Some Conditional Correlation Inequalities for Percolation and Related Processes | |
| dc.type | text |