Invariant Gibbs measure for Anderson nonlinear wave equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910905855377408 |
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| author | Barashkov, Nikolay De Vecchi, Francesco C. Zachhuber, Immanuel |
| author_facet | Barashkov, Nikolay De Vecchi, Francesco C. Zachhuber, Immanuel |
| contents | We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field exploiting the stochastic optimal control formulation of Gibbs measures. Using this coupling, we define the renormalized powers of the Anderson free field and we prove that the associated quartic Gibbs measure is invariant under the flow of a nonlinear wave equation with renormalized cubic nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01635 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant Gibbs measure for Anderson nonlinear wave equation Barashkov, Nikolay De Vecchi, Francesco C. Zachhuber, Immanuel Probability Mathematical Physics Analysis of PDEs 60H30, 35L71 (Primary), 28C20, 60L40 We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field exploiting the stochastic optimal control formulation of Gibbs measures. Using this coupling, we define the renormalized powers of the Anderson free field and we prove that the associated quartic Gibbs measure is invariant under the flow of a nonlinear wave equation with renormalized cubic nonlinearity. |
| title | Invariant Gibbs measure for Anderson nonlinear wave equation |
| topic | Probability Mathematical Physics Analysis of PDEs 60H30, 35L71 (Primary), 28C20, 60L40 |
| url | https://arxiv.org/abs/2309.01635 |