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Abstract / Description of output
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.
Original language | English |
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Pages (from-to) | 343-379 |
Number of pages | 37 |
Journal | Probability and Mathematical Physics |
Volume | 3 |
Issue number | 2 |
DOIs | |
Publication status | Published - 9 Jul 2022 |
Keywords / Materials (for Non-textual outputs)
- nonlinear wave equation
- Gaussian measure
- quasi-invariance
- Euclidean quantum field theory
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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research