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July 2011 On monochromatic arm exponents for 2D critical percolation
Vincent Beffara, Pierre Nolin
Ann. Probab. 39(4): 1286-1304 (July 2011). DOI: 10.1214/10-AOP581

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. "On monochromatic arm exponents for 2D critical percolation." Ann. Probab. 39 (4) 1286 - 1304, July 2011. https://doi.org/10.1214/10-AOP581

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1225.82029
MathSciNet: MR2857240
Digital Object Identifier: 10.1214/10-AOP581

Subjects:
Primary: 60K35 , 82B43

Keywords: Critical exponent , percolation , Scaling limit

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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