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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.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00396822 Contributor : Vincent BeffaraConnect in order to contact the contributor Submitted on : Thursday, January 25, 2018 - 6:52:11 PM Last modification on : Tuesday, October 19, 2021 - 11:05:59 AM Long-term archiving on: : Friday, May 25, 2018 - 7:03:10 AM
Vincent Beffara, Pierre Nolin. On monochromatic arm exponents for 2D critical percolation. Annals of Probability, Institute of Mathematical Statistics, 2011, 39 (4), pp.1286 - 1304. ⟨10.1214/10-AOP581⟩. ⟨ensl-00396822v4⟩