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arXiv · 0906.5328

The Global Geometry of Stochastic Lœwner Evolutions

Roland M. Friedrich
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Abstract

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.

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Roland M. Friedrich. 2009-06-29. The Global Geometry of Stochastic Lœwner Evolutions. https://arxiv.org/abs/0906.5328

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