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.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Albeverio, Sergio; Hu, YZ; Röckner, MichaelUniBi; Zhou, XY
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.
Stichworte
two-dimensional polymer measure; Dirichlet forms; ergodicity; diffusion processes; closability; quasi-invariance
Erscheinungsjahr
1999
Zeitschriftentitel
Applied Mathematics and Optimization
Band
40
Ausgabe
3
Seite(n)
341-354
ISSN
0095-4616
Page URI
https://pub.uni-bielefeld.de/record/1622169

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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.