Hyperbolic sine-Gordon model beyond the first threshold
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915277123354624 |
|---|---|
| author | Zine, Younes |
| author_facet | Zine, Younes |
| contents | We study the hyperbolic sine-Gordon model, with a parameter $\be^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. By introducing a physical space approach to the Fourier restriction norm method and establishing nonlinear dispersive smoothing for the imaginary multiplicative Gaussian chaos, we construct invariant Gibbs dynamics for the hyperbolic sine-Gordon model beyond the first threshold $\be^2 = 2π$. The deterministic step of our argument hinges on establishing key bilinear estimates, featuring weighted bounds for cone multipliers. Moreover, the probabilistic component involves a careful analysis of the imaginary Gaussian multiplicative chaos and reduces to integrating singularities along space-time light cones. As a by-product of our proof, we identify $\be^2 = 6π$ as a critical threshold for the hyperbolic sine-Gordon model, which is quite surprising given that the associated parabolic model has a critical threshold at $\be^2 =8π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic sine-Gordon model beyond the first threshold Zine, Younes Analysis of PDEs Mathematical Physics Probability 35L71, 60H15, 42B37, 81T08 We study the hyperbolic sine-Gordon model, with a parameter $\be^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. By introducing a physical space approach to the Fourier restriction norm method and establishing nonlinear dispersive smoothing for the imaginary multiplicative Gaussian chaos, we construct invariant Gibbs dynamics for the hyperbolic sine-Gordon model beyond the first threshold $\be^2 = 2π$. The deterministic step of our argument hinges on establishing key bilinear estimates, featuring weighted bounds for cone multipliers. Moreover, the probabilistic component involves a careful analysis of the imaginary Gaussian multiplicative chaos and reduces to integrating singularities along space-time light cones. As a by-product of our proof, we identify $\be^2 = 6π$ as a critical threshold for the hyperbolic sine-Gordon model, which is quite surprising given that the associated parabolic model has a critical threshold at $\be^2 =8π$. |
| title | Hyperbolic sine-Gordon model beyond the first threshold |
| topic | Analysis of PDEs Mathematical Physics Probability 35L71, 60H15, 42B37, 81T08 |
| url | https://arxiv.org/abs/2504.07944 |