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.
"On monochromatic arm exponents for 2D critical percolation." Ann. Probab. 39 (4) 1286 - 1304, July 2011. https://doi.org/10.1214/10-AOP581