Extreme nesting in the conformal loop ensemble

• Miller, Jason ^[1] ; Watson, Samuel S. ^[1] ; Wilson, David B ^[1]
  1. [1] The Microsoft Research - University of Trento Centre for Computational and Systems Biology

     The Microsoft Research - University of Trento Centre for Computational and Systems Biology

     Trento, Italia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 2, 2016, págs. 1013-1052
• Idioma: inglés
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• Resumen

  • The conformal loop ensemble CLEκ with parameter 8/3<κ<8 is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given κ and ν, we compute the almost-sure Hausdorff dimension of the set of points z for which the number of CLE loops surrounding the disk of radius ε centered at z has asymptotic growth νlog(1/ε) as ε→0. By extending these results to a setting in which the loops are given i.i.d. weights, we give a CLE-based treatment of the extremes of the Gaussian free field.