On monochromatic arm exponents for 2D critical percolation

Vincent Beffara (1) , Pierre Nolin (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 CIMS - Courant Institute of Mathematical Sciences [New York]

We investigate the so-called "monochromatic arm exponents" for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j+1)-arm exponents.

Keywords: Percolation; Critical exponents; Backbone exponent; Correlation inequalities

Domains: Mathematics [math]; Probability [math.PR]

Vincent Beffara, Pierre Nolin. On monochromatic arm exponents for 2D critical percolation. Annals of Probability, 2011, 39 (4), pp.1286 - 1304. ⟨10.1214/10-AOP581⟩. ⟨ensl-00396822v4⟩