Stochastic Quantization of the Two-Dimensional Polymer Measure

Stochastic Quantization of the Two-Dimensional Polymer Measure We prove that there exists a diffusion process whose invariant measure is the two-dimensional polymer measure ν g . The diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. We prove the closability of the appropriate pre-Dirichlet form which is of gradient type, using a general closability result by two of the authors. This result does not require an integration by parts formula (which does not hold for the two-dimensional polymer measure ν g ) but requires the quasi-invariance of ν g along a basis of vectors in the classical Cameron—Martin space such that the Radon—Nikodym derivatives (have versions which) form a continuous process. We also show the Dirichlet form to be irreducible or equivalently that the diffusion process is ergodic under time translations. Applied Mathematics and Optimization Springer Journals

Stochastic Quantization of the Two-Dimensional Polymer Measure

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Copyright © Inc. by 1999 Springer-Verlag New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
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