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A stochastic control approach to Sine Gordon EQFT
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abstract
We study the Sine-Gordon model for $\beta^{2}< 4 \pi$ in infinite volume. We give a variatonal characterization of it's laplace transform, and deduce from this large deviations. Along the way we obtain estimates which are strong enough to obtain a proof of the Osterwalder-Schrader axioms including exponential decay of correlations as a byproduct. Our method is based on the Boue-Dupuis formula with an emphasis on the stochastic control structure of the problem.
Forward citations
Cited by 3 Pith papers
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An FBSDE Construction of the Sine-Gordon EQFT for $\beta^{2} < \frac{6}{7}\, 8\pi$ and Perturbative Renormalization in the Full Subcritical Regime
The 2D finite-volume sine-Gordon measure is constructed for β² < (6/7)·8π via a weak FBSDE/control problem, with an order-by-order renormalization-flow analysis valid for all β² < 8π.
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A quadratic BSDE approach to normalization for the finite volume 2D sine-Gordon model in the finite ultraviolet regime
A quadratic backward stochastic differential equation is used to define and prove weak convergence of an ultraviolet-regulated 2D sine-Gordon measure that is absolutely continuous with respect to the Gaussian free fie...
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A simple construction of the sine-Gordon model via stochastic quantization
Renormalized sine-Gordon measures are shown to be tight below a critical coupling via parabolic stochastic quantization, with a new pathwise global well-posedness result for the hyperbolic model in a smaller range.
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