Stochastic quantization of the two-dimensional polymer measure
Albeverio, Sergio
Albeverio
Sergio
Hu, YZ
Hu
YZ
Röckner, Michael
Röckner
Michael
Zhou, XY
Zhou
XY
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.
40
3
341-354
341-354
Springer
1999