Effect of random time changes on Loewner hulls

  • Kei Kobayashi

    Fordham University, New York, USA
  • Joan Lind

    The University of Tennessee, Knoxville, USA
  • Andrew Starnes

    University of Hartford, West Hartford, USA
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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 -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 for generates a hull that leaves the real line tangentially.

Cite this article

Kei Kobayashi, Joan Lind, Andrew Starnes, Effect of random time changes on Loewner hulls. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 771–790

DOI 10.4171/RMI/1148