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arxiv: 1609.06626 · v2 · pith:VZYBYTRCnew · submitted 2016-09-21 · 🧮 math.PR

Arm events in two-dimensional invasion percolation

classification 🧮 math.PR
keywords percolationinvasioneventscolorcriticalexistenceinvadedprobabilities
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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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