## Abstract

Consider critical site percolation on Zd with d ≥ 2. Cerf (Ann. Probab. 43 (2015) 2458-2480) pointed out that from classical work by Aizenman, Kesten and Newman (Comm. Math. Phys. 111 (1987) 505-532) and Gandolfi, Grimmett and Russo (Comm. Math. Phys. 114 (1988) 549-552) one can obtain that the two-arms exponent is at least 1/2. The paper by Cerf slightly improves that lower bound. Except for d = 2 and for high d, no upper bound for this exponent seems to be known in the literature so far (not even implicitly). We show that the distance-n two-arms probability is at least cn-(d2+4d-2) (with c > 0 a constant which depends on d), thus giving an upper bound d2+ 4d - 2 for the above mentioned exponent.

Original language | English |
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Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 58 |

Issue number | 1 |

Early online date | 2 Feb 2022 |

DOIs | |

Publication status | Published - Feb 2022 |

### Bibliographical note

Publisher Copyright:© Association des Publications de l'Institut Henri Poincaré, 2022.

## Keywords

- Critical exponent
- Critical percolation