Higher correlation inequalities

Abstract

We prove a correlation inequality for n increasing functions on a distributive lattice, which for n = 2 reduces to a special case of the FKG inequality. The key new idea is to reformulate the inequalities for all n into a single positivity statement in the ring of formal power series. We also conjecture that our results hold in greater generality.

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Correspondence to Siddhartha Sahi.

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Sahi, S. Higher correlation inequalities. Combinatorica 28, 209–227 (2008). https://doi.org/10.1007/s00493-008-2249-5

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Mathematics Subject Classification (2000)

  • 05A20
  • 26D07
  • 60E15
  • 82B20