On monochromatic arm exponents for 2D critical percolation

Abstract

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.

Published in at http://dx.doi.org/10.1214/10-AOP581 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)