Vincent Beffara, Pierre Nolin
Published 2009-06-19, updated 2012-11-15Version 4
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.
Comments: 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)
Journal: Annals of Probability 2011, Vol. 39, No. 4, 1286-1304
The lowest crossing in 2D critical percolation
On the size of the largest cluster in 2D critical percolation
The gaps between the sizes of large clusters in 2D critical percolation
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