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math.PR2004
Some Conditional Correlation Inequalities for Percolation and Related Processes
Jacob van den Berg, Olle Haggstrom, Jeff Kahn
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 th…
math.PR2000
A signal-recovery system: asymptotic properties and construction of an infinite volume limit
Jacob van den Berg, Balint Toth
We consider a linear sequence of `nodes', each of which can be in state 0 (`off') or 1 (`on'). Signals from outside are sent to the rightmost node and travel instantaneously as far…