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We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in the previous work on the two-dimensional case, we employ a simultaneous renormalization on the energy functional and its time derivative. Two new ingredients in the three-dimensional case are (i) the construction of the weighted Gaussian measures, based on a variational formula for the partition function inspired by Barashkov and Gubinelli~(2018), and (ii) an improved argument in controlling the growth of the truncated weighted Gaussian measures, where we combine a deterministic growth bound of solutions with stochastic estimates on random distributions.
|Number of pages||36|
|Journal||Probability and Mathematical Physics|
|Publication status||Accepted/In press - 10 Jul 2021|
- nonlinear wave equation
- Gaussian measure
- Euclidean quantum field theory
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- 1 Finished
1/03/15 → 29/02/20