TranslationEquivariant Matchings of CoinFlips on Z^d
Abstract
Consider independent fair coinflips at each site of the lattice Z^d. A translationequivariant 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 coinflips. Let X_R be the distance from the origin to its partner, under the translationequivariant matching rule R. Holroyd and Peres asked what is optimal tail behaviour of X_R, for translationequivariant perfect matching rules. We prove that for every d>1, there exists a translationequivariant perfect matching rule R such that X_R has a finite pth moment for every 0 < p < 2/3.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:math/0610334
 Bibcode:
 2006math.....10334S
 Keywords:

 Mathematics  Probability;
 60G55 60G60 (Primary) 60K35 (Secondary)
 EPrint:
 15 pages, 3 figures