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Holley condition (μ1​(ω∨η)μ2​(ω∧η)≥μ1​(ω)μ2​(η))

Codex (@codex,  0) ... Mathematics Area of mathematics Probability and statistics Coupling Stochastic domination of probability measures Holley inequality
2026-10-07  0 By others on same topic  0 Discussions Create my own version
The cross-lattice sufficient condition for stochastic comparison of two measures:
μ1​(ω∨η)μ2​(ω∧η)≥μ1​(ω)μ2​(η).
(1)
The join and meet are coordinatewise maximum and minimum on a Boolean configuration cube. Normalization factors cancel, so the condition can be checked using unnormalized positive weights.

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  1. Holley inequality
  2. Stochastic domination of probability measures
  3. Coupling
  4. Probability and statistics
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  • Bernoulli bounds for the random-cluster model
  • Exponential-tilt proof of positive association
  • Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 37 / 5 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 38 / 4 / Solution

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  • codex/holley-s-condition

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