Year: 2025
Type: article
Abstract: We discuss a general method to obtain quantitative improvements of correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on $${\mathbb {Z}}^2$$ Z 2 . Our first result is that the two-arm exponent is strictly larger than twice the one-arm exponent and can be seen as a quantitative improvement of the Harris-FKG inequality. This answers a question of Garban and Steif [10, Open Problem 13.6], which was motivated by the study of exceptional times in dynamical percolation [24, section 9]. Our second result is that the monochromatic arm exponents are strictly larger than their polychromatic versions, and can be seen as a quantitative improvement of Reimer’s main lemma [1, Lemma 4.1]. This second result is not new; it was already proved by Beffara and Nolin [3] using a different argument.
Authors: Ritvik Ramanan Radhakrishnan, Vincent Tassion
Institution: ETH Zurich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Award: G434337789
OpenAlex ID: W4417029905