Lattice embeddings in percolation

Details Lattice embeddings in percolation Lattice embeddings in percolation

2010-03-20

arxiv.org/abs/1003.3950v1

Mathematics

Probability

Scientific paper

Does there exist a Lipschitz injection of Z^d into the open set of a site percolation process on Z^D, if the percolation parameter p is sufficiently close to 1? We prove a negative answer when d=D, and also when d>=2 if the Lipschitz constant M is required to be 1. Earlier work of Dirr, Dondl, Grimmett, Holroyd, and Scheutzow yields a positive answer for d

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