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math.PR2018
Finitary isomorphisms of Poisson point processes
Terry Soo, Amanda Wilkens
As part of a general theory for the isomorphism problem for actions of amenable groups, Ornstein and Weiss (J. Anal. Math. 48:1-141,1987) proved that any two Poisson point processe…
math.PR2006
A Nonmeasurable Set from Coin Flips
Alexander E. Holroyd, Terry Soo
In this note we give an example of a nonmeasurable set in the probability space for an infinite sequence of coin flips. The example arises naturally from the notion of an equivaria…
math.PR2006★ 2 cited
Translation-Equivariant Matchings of Coin-Flips on Z^d
Terry Soo
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 translation…