On monochromatic arm exponents for 2D critical percolation

Details On monochromatic arm exponents for 2D critical percolation On monochromatic arm exponents for 2D critical percolation

2009-06-19

arxiv.org/abs/0906.3570v3

Mathematics

Probability

Slight modifications following the recommendations of the referee

Scientific paper

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.

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