Translation-Equivariant Matchings of Coin Flips on ℤ d

  title={Translation-Equivariant Matchings of Coin Flips on ℤ d},
  author={Terry Soo},
  journal={Advances in Applied Probability},
  pages={69 - 82}
  • Terry Soo
  • Published 2010
  • Mathematics
  • Advances in Applied Probability
Consider independent fair coin flips at each site of the lattice ℤ d . A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of ℤ d and is given by a deterministic function of the coin flips. Let Z Φ be the distance from the origin to its partner, under the translation-equivariant matching rule Φ. Holroyd and Peres (2005) asked, what is the optimal tail behaviour of Z Φ for translation-equivariant perfect matching rules? We prove that… Expand
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