On monochromatic arm exponents for 2D critical percolation

Vincent Beffara; Pierre Nolin

doi:10.1214/10-aop581

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arXiv · 0906.3570

On monochromatic arm exponents for 2D critical percolation

Vincent Beffara·Pierre Nolin

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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.

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Vincent Beffara, Pierre Nolin. 2009-06-19. On monochromatic arm exponents for 2D critical percolation. https://doi.org/10.1214/10-aop581

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