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Extreme nesting in the conformal loop ensemble. (English) Zbl 1347.60061
The authors study the extreme nesting in the conformal loop ensemble (CLE), beginning with a review on the large deviation estimates (see [A. Dembo and O. Zeitouni, Large deviations techniques and applications. 2nd ed. Berlin: Springer (2010; Zbl 1177.60035)]).
It is shown that it suffices to describe the CLE nesting behaviour at single points to give the upper bound, while for the lower bound a subset of special points is investigated, that have full dimension and are only weakly correlated. Also, a Hausdorff dimension lower bound is given as well.

MSC:
60G70 Extreme value theory; extremal stochastic processes
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
60F10 Large deviations
60D05 Geometric probability and stochastic geometry
60G60 Random fields
60G15 Gaussian processes
37A25 Ergodicity, mixing, rates of mixing
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