Stochastic quantization of the two-dimensional polymer measure

Albeverio S, Hu YZ, Röckner M, Zhou XY (1999)
Applied Mathematics and Optimization 40(3): 341-354.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We prove that there exists a diffusion process whose invariant measure is the two-dimensional polymer measure nu(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 nu(g)) but requires the quasi-invariance of nu(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.
Erscheinungsjahr
Zeitschriftentitel
Applied Mathematics and Optimization
Band
40
Ausgabe
3
Seite(n)
341-354
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Albeverio S, Hu YZ, Röckner M, Zhou XY. Stochastic quantization of the two-dimensional polymer measure. Applied Mathematics and Optimization. 1999;40(3):341-354.
Albeverio, S., Hu, Y. Z., Röckner, M., & Zhou, X. Y. (1999). Stochastic quantization of the two-dimensional polymer measure. Applied Mathematics and Optimization, 40(3), 341-354. doi:10.1007/s002459900129
Albeverio, S., Hu, Y. Z., Röckner, M., and Zhou, X. Y. (1999). Stochastic quantization of the two-dimensional polymer measure. Applied Mathematics and Optimization 40, 341-354.
Albeverio, S., et al., 1999. Stochastic quantization of the two-dimensional polymer measure. Applied Mathematics and Optimization, 40(3), p 341-354.
S. Albeverio, et al., “Stochastic quantization of the two-dimensional polymer measure”, Applied Mathematics and Optimization, vol. 40, 1999, pp. 341-354.
Albeverio, S., Hu, Y.Z., Röckner, M., Zhou, X.Y.: Stochastic quantization of the two-dimensional polymer measure. Applied Mathematics and Optimization. 40, 341-354 (1999).
Albeverio, Sergio, Hu, YZ, Röckner, Michael, and Zhou, XY. “Stochastic quantization of the two-dimensional polymer measure”. Applied Mathematics and Optimization 40.3 (1999): 341-354.