Translation - Equivariant Matchings of Coin
نویسنده
چکیده
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 [9] asked what is the optimal tail behaviour of Z Φ , for translation-equivariant perfect matching rules. We prove that for every d ≥ 2, there exists a translation-equivariant perfect matching rule Φ such that EZ 2 3 −ε Φ < ∞ for every ε > 0.
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