Details

Autor(en) / Beteiligte

• Kobayashi, Kei
• Lind, Joan
• Starnes, Andrew

Titel

Effect of random time changes on Loewner hulls

Ist Teil von

• Revista matemática iberoamericana, 2020-01, Vol.36 (3), p.771-790

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.