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Embeddings, entanglement, and percolation

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Can there exist a monotone embedding of one infinite random word inside another, with bounded gaps? What can be said about the critical point for the existence of an infinite `entangled’ set of open edges in the percolation model on the cubic lattice? These two questions are connected through a new type of percolation process, called `Lipschitz percolation’. It will be shown how to embed higher-dimensional words, and to obtain the best (so far) lower bound for the entanglement critical point.

This talk is part of the Probability series.

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