A correlation inequality for connection events in percolation

Authors
van den Berg, J Kahn, J
Citation
J. Van Den Berg et J. Kahn, A correlation inequality for connection events in percolation, ANN PROBAB, 29(1), 2001, pp. 123-126
Citations number
6
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
29
Issue
1
Year of publication
2001
Pages
123 - 126
Database
ISI
SICI code
0091-1798(200101)29:1<123:ACIFCE>2.0.ZU;2-X
Abstract
It is well-known in percolation theory (and intuitively plausible) that two events of the form "there is an open path from s to a" are positively corr elated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form "there is no open path from s to t .".