Arm events in two-dimensional invasion percolation

Michael Damron; Jack Hanson; Philippe Sosoe

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arXiv · 1609.06626

Arm events in two-dimensional invasion percolation

Michael Damron·Jack Hanson·Philippe Sosoe

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Abstract

We compare the probabilities of arm events in two-dimensional invasion percolation to those in critical percolation. Arm events are defined by the existence of a prescribed color sequence of invaded and non-invaded connections from the origin to distance n. We find that, for sequences of a particular form, arm probabilities in invasion percolation and critical percolation are comparable, uniformly in n, while they differ by a power of n for all others. A corollary of our results is the existence, on the triangular lattice, of arm exponents for invasion percolation, for any color sequence with at least two open (invaded) entries.

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Michael Damron, Jack Hanson, Philippe Sosoe. 2016-09-21. Arm events in two-dimensional invasion percolation. https://arxiv.org/abs/1609.06626

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