Resumen de Extreme nesting in the conformal loop ensemble
Jason Miller, Samuel S. Watson, David B. Wilson
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.
