The Global Geometry of Stochastic Lœwner Evolutions

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.

31 pages, 5 figures, conference proceedings

References in corpus (3)

• Vertex Algebras and Algebraic Curves
• On Conformal Field Theory and Stochastic Loewner Evolution
• On Connections of Conformal Field Theory and Stochastic Lœwner Evolution

Cited by in corpus (5)

• Calculus on manifolds of conformal maps and CFT
• Local martingales associated with Schramm-Loewner evolutions with internal symmetry
• Univalence and holomorphic extension of the solution to $\omega$-controlled Loewner-Kufarev equations
• The Maxwell-Boltzmann Distribution is not the Equilibrium on a Hyperboloid
• Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian