Revista Matemática Iberoamericana
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Effect of random time changes on Loewner hullsKei Kobayashi, Joan Lind and Andrew Starnes (1) Fordham University, New York, USA
(2) The University of Tennessee, Knoxville, USA
(3) University of Hartford, West Hartford, USA
Loewner hulls are determined by their real-valued driving functions. We study the geometric effect on the Loewner hulls when the driving function is composed with a random time change, such as the inverse of an $\alpha$-stable subordinator. In contrast to SLE, we show that for a large class of random time changes, the time-changed Brownian motion process does not generate a simple curve. Further we develop criteria which can be applied in many situations to determine whether the Loewner hull generated by a time-changed driving function is simple or non-simple. To aid our analysis of an example with a time-changed deterministic driving function, we prove a deterministic result that a driving function that moves faster than $at^r$ for $r \in (0, 1/2)$ generates a hull that leaves the real line tangentially.
Keywords: Loewner evolution, random time change, inverse subordinator, time-changed Brownian motion
Kobayashi Kei, Lind Joan, Starnes Andrew: Effect of random time changes on Loewner hulls. Rev. Mat. Iberoam. Electronically published on October 15, 2019. doi: 10.4171/rmi/1148 (to appear in print)