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Abstract / Description of output
We prove quasiinvariance of Gaussian measures supported on Sobolev spaces under the dynamics of the threedimensional defocusing cubic nonlinear wave equation. As in the previous work on the twodimensional case, we employ a simultaneous renormalization on the energy functional and its time derivative. Two new ingredients in the threedimensional 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 

Pages (fromto)  343379 
Number of pages  37 
Journal  Probability and Mathematical Physics 
Volume  3 
Issue number  2 
DOIs  
Publication status  Published  9 Jul 2022 
Keywords / Materials (for Nontextual outputs)
 nonlinear wave equation
 Gaussian measure
 quasiinvariance
 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