Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916859539881984 |
|---|---|
| author | Albeverio, Sergio Kusuoka, Seiichiro Liang, Song Nakashima, Makoto |
| author_facet | Albeverio, Sergio Kusuoka, Seiichiro Liang, Song Nakashima, Makoto |
| contents | We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $ν_λ$ for all $λ>0$. We follow in part a previous incomplete unpublished work of the first named author with M. Röckner and X.Y. Zhou. For the construction of $ν_λ$ we rely on previous work by J. Westwater, E. Bolthausen and X.Y. Zhou. Using $ν_λ$, the diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. The closability of the appropriate pre-Dirichlet form which is of gradient type is proven, by using a general closability result in [AR89a]. This result does not require an integration by parts formula (which does not even hold for the two-dimensional polymer measure $ν_λ$) but requires the quasi-invariance of $ν_λ$ along a basis of vectors in the classical Cameron-Martin space such that the Radon-Nikodym derivatives have versions which form a continuous process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05797 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method Albeverio, Sergio Kusuoka, Seiichiro Liang, Song Nakashima, Makoto Probability Mathematical Physics 81S20, 60J65, 60J46, 60H30 We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $ν_λ$ for all $λ>0$. We follow in part a previous incomplete unpublished work of the first named author with M. Röckner and X.Y. Zhou. For the construction of $ν_λ$ we rely on previous work by J. Westwater, E. Bolthausen and X.Y. Zhou. Using $ν_λ$, the diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. The closability of the appropriate pre-Dirichlet form which is of gradient type is proven, by using a general closability result in [AR89a]. This result does not require an integration by parts formula (which does not even hold for the two-dimensional polymer measure $ν_λ$) but requires the quasi-invariance of $ν_λ$ along a basis of vectors in the classical Cameron-Martin space such that the Radon-Nikodym derivatives have versions which form a continuous process. |
| title | Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method |
| topic | Probability Mathematical Physics 81S20, 60J65, 60J46, 60H30 |
| url | https://arxiv.org/abs/2311.05797 |