About: Ahlswede–Daykin inequality

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The Ahlswede–Daykin inequality, also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It is a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method). The inequality states that if are nonnegative functions on a finite distributive lattice such that for all x, y in the lattice, then for all subsets X, Y of the lattice, where and For a proof, see the original article or.

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  • The Ahlswede–Daykin inequality, also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It is a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method). The inequality states that if are nonnegative functions on a finite distributive lattice such that for all x, y in the lattice, then for all subsets X, Y of the lattice, where and The Ahlswede–Daykin inequality can be used to provide a short proof of both the Holley inequality and the FKG inequality. It also implies the XYZ inequality. For a proof, see the original article or. (en)
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  • Peter Fishburn (en)
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  • P.C. (en)
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  • Fishburn (en)
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  • Ahlswede–Daykin inequality (en)
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  • The Ahlswede–Daykin inequality, also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It is a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method). The inequality states that if are nonnegative functions on a finite distributive lattice such that for all x, y in the lattice, then for all subsets X, Y of the lattice, where and For a proof, see the original article or. (en)
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  • Ahlswede–Daykin inequality (en)
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