A Conformally Invariant Growth Process of SLE Excursions

作者：Pete, Gabor^*; Wu, Hao

来源：Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2018, 15(2): 851-874.

DOI：10.30757/ALEA.v15-32

• Schramm Loewner evolution
• Hausdorff dimension

We construct an aggregation process of chordal SLEk excursions in the unit disk, starting from the boundary, growing towards all inner points simultaneously, invariant under all conformal self- maps of the disk. We prove that this conformal growth process of excursions, abbreviated as CGE(k), exists kappa is an element of [0, 4), and that it does not create additional fractalness: the Hausdor ff dimension of the closure of all the SLEk arcs attached is 1 + k/8 almost surely. We determine the dimension of points that are approached by CGE(k) at an atypical rate.

• 出版日期2018
• 单位清华大学