English

Arm events in two-dimensional invasion percolation

Probability 2017-08-17 v2

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.

Keywords

Cite

@article{arxiv.1609.06626,
  title  = {Arm events in two-dimensional invasion percolation},
  author = {Michael Damron and Jack Hanson and Philippe Sosoe},
  journal= {arXiv preprint arXiv:1609.06626},
  year   = {2017}
}

Comments

37 pages, 9 figures; typos corrected

R2 v1 2026-06-22T15:56:49.413Z