Effect of random time changes on Loewner hulls

Kei Kobayashi ^[1] ; Joan Lind ^[3] ; Andrew Starnes ^[2]
1. [1] Fordham University
  
  Fordham University
  
  Estados Unidos
2. [2] University of Hartford
  
  University of Hartford
  
  Town of West Hartford, Estados Unidos
3. [3] The University of Tennessee
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Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 3, 2020, págs. 771-790
Idioma: inglés
DOI: 10.4171/rmi/1148
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Resumen
- 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 α-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 atr for r∈(0,1/2) generates a hull that leaves the real line tangentially.