English

On monochromatic arm exponents for 2D critical percolation

Probability 2012-11-16 v4

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.

Keywords

Cite

@article{arxiv.0906.3570,
  title  = {On monochromatic arm exponents for 2D critical percolation},
  author = {Vincent Beffara and Pierre Nolin},
  journal= {arXiv preprint arXiv:0906.3570},
  year   = {2012}
}

Comments

Published in at http://dx.doi.org/10.1214/10-AOP581 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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