Extra heads and invariant allocations

@article{Holroyd2005ExtraHA,
  title={Extra heads and invariant allocations},
  author={Alexander E. Holroyd and Yuval Peres},
  journal={Annals of Probability},
  year={2005},
  volume={33},
  pages={31-52}
}
Let n be an ergodic simple point process on E d and let n* be its Palm version. Thorisson [Ann. Probab. 24 (1996) 2057-2064] proved that there exists a shift coupling of Π and n*; that is, one can select a (random) point Y of n such that translating n by -Y yields a configuration whose law is that of Π*. We construct shift couplings in which Y and Π* are functions of Π, and prove that there is no shift coupling in which n is a function of Π*. The key ingredient is a deterministic translation… Expand

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