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Journal Articles Annals of Probability Year : 2011

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.
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Dates and versions

ensl-00396822 , version 1 (19-06-2009)
ensl-00396822 , version 2 (22-06-2009)
ensl-00396822 , version 3 (06-05-2010)
ensl-00396822 , version 4 (25-01-2018)

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Vincent Beffara, Pierre Nolin. On monochromatic arm exponents for 2D critical percolation. Annals of Probability, 2011, 39 (4), pp.1286 - 1304. ⟨10.1214/10-AOP581⟩. ⟨ensl-00396822v4⟩
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