The Annals of Probability

On monochromatic arm exponents for 2D critical percolation

Vincent Beffara and Pierre Nolin

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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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Ann. Probab., Volume 39, Number 4 (2011), 1286-1304.

First available in Project Euclid: 5 August 2011

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Zentralblatt MATH identifier

Primary: 82B43: Percolation [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Percolation critical exponent scaling limit


Beffara, Vincent; Nolin, Pierre. On monochromatic arm exponents for 2D critical percolation. Ann. Probab. 39 (2011), no. 4, 1286--1304. doi:10.1214/10-AOP581.

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