Conditional correlation inequalities for percolation and contact processes
Markov Chains in Algorithms and Statistical Physics
February 04, 2005 11:50 AM to 12:35 PM
Speakers:
|
 |
Abstract: |
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).
Joint work with J. Kahn and O. Haggstrom.
|
|
|
