Advanced Studies in Pure Mathematics

The global geometry of stochastic Lœwner evolutions

Roland Friedrich

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In this article we develop a concise description of the global geometry which is underlying the universal construction of all possible generalised Stochastic Lœwner Evolutions. The main ingredient is the Universal Grassmannian of Sato–Segal–Wilson. We illustrate the situation in the case of univalent functions defined on the unit disc and the classical Schramm–Lœwner stochastic differential equation. In particular we show how the Virasoro algebra acts on probability measures. This approach provides the natural connection with Conformal Field Theory and Integrable Systems.

Article information

Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 79-117

Received: 17 April 2009
Revised: 18 September 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document euclid.aspm/1543086313

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82B99: None of the above, but in this section 32C99: None of the above, but in this section 60J99: None of the above, but in this section 81T40: Two-dimensional field theories, conformal field theories, etc.

Complex variables stochastic analysis Conformal Field Theory


Friedrich, Roland. The global geometry of stochastic Lœwner evolutions. Probabilistic Approach to Geometry, 79--117, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710079.

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