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Positive association of the random-cluster model
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Probability and statistics
Probability theory
Percolation theory
Site percolation
Dependent percolation
Random-cluster model
2026-09-28
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For
0
≤
p
≤
1
and
q
≥
1
, the
FKG inequality
implies that increasing
functions
of
a
random-cluster configuration have nonnegative
covariance
. The conclusion can fail for
0
<
q
<
1
.
Ancestors
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Random-cluster model
Dependent percolation
Site percolation
Percolation theory
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 204
/
3
/
Solution
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