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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