Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 1 (2017), 151-164.

Loewner deformations driven by the Weierstrass function

Joan Lind and Jessica Robins

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The Loewner differential equation provides a way of encoding growing families of sets into continuous real-valued functions. Most famously, Schramm–Loewner evolution (SLE) consists of the growing random families of sets that are encoded via the Loewner equation by a multiple of Brownian motion. The purpose of this paper is to study the families of sets encoded by a multiple of the Weierstrass function, which is a deterministic analog of Brownian motion. We prove that there is a phase transition in this setting, just as there is in the SLE setting.

Article information

Involve, Volume 10, Number 1 (2017), 151-164.

Received: 15 September 2015
Accepted: 13 December 2015
First available in Project Euclid: 22 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C35: General theory of conformal mappings

Loewner evolution Weierstrass function


Lind, Joan; Robins, Jessica. Loewner deformations driven by the Weierstrass function. Involve 10 (2017), no. 1, 151--164. doi:10.2140/involve.2017.10.151.

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