Z^d上抛硬币的平移等变匹配
Translation-Equivariant Matchings of Coin-Flips on Z^d
摘要：
考虑在格Z^d的每个位置处的独立公平硬币翻转。反等变匹配规则是一种正面到反面的完美匹配，它与Z^d的平移互换，并由硬币翻转的确定性函数给出。设X_R是在平行等变匹配规则R下，从原点到其配对点的距离。Holroyd和Peres提出了一个问题，即对于双等变完美匹配规则，X_R的最优尾部行为是什么。证明了对任意d>1，存在一个双等变完美匹配规则R，使得对任意0 < p < 2/3，X_R有有限的p阶矩。
英文摘要：
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 X_R be the distance from the origin to its partner, under the translation-equivariant matching rule R. Holroyd and Peres asked what is optimal tail behaviour of X_R, for translation-equivariant perfect matching rules. We prove that for every d>1, there exists a translation-equivariant perfect matching rule R such that X_R has a finite p-th moment for every 0 < p < 2/3.
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