The Loewner equation: Maps and shapes

Journal of Statistical Physics

Volumn 114, Issue 5-6, 2004, Pages 1183-1198

  Gruzberg, Ilya A ^a   Kadanoff, Leo P ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Conformal field theory; Criticality in two dimensions; Stochastic Loewner evolution

Indexed keywords

EID: 3142773838     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000013973.40984.3b     Document Type: Article

References (18)

1. As stated in the work of D. Marshall and S. Rohde (see "The Loewner differential equation and slit mappings," available online at URL http://www.math.washington.edu/~rohde/), the behavior changes qualitatively when the coefficient in front of the singularity passes through a critical value. In ref. 2, a few exact solutions of the Loewner evolution were obtained including one for a square root singularity. According to this paper the critical value is four.
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