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On monochromatic arm exponents for 2D critical percolation. (English) Zbl 1225.82029
Summary: 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.

MSC:
82B43 Percolation
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B27 Critical phenomena in equilibrium statistical mechanics
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