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On Malliavin measures, SLE, and CFT. (English) Zbl 1155.81367
Proc. Steklov Inst. Math. 258, 100-146 (2007) and Tr. Mat. Inst. Steklova 258, 107-153 (2007).
Summary: This paper is dedicated to the 70th birthday of V. Arnol’d. The paper is motivated by emerging connections between the conformal field theory (CFT) on the one hand and stochastic Löwner evolution (SLE) processes and measures that play the role of the Haar measures for the diffeomorphism group of a circle, on the other hand. We attempt to build a framework for widely spread beliefs that SLE processes would provide a picture of phase separation in a small massive perturbation of the CFT.

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
57M50 General geometric structures on low-dimensional manifolds
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
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