Develops an arborification map on decorated trees to compute cancellations in random-data dispersive PDEs, enabling results on wave turbulence and 3D cubic wave equation Gibbs measure invariance.
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Constructs uniform estimates and explicit counterterm for the renormalized stochastic thin-film equation in the full subcritical regime across dimensions d ≥ 1.
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Cancellations for dispersive PDEs with random initial data
Develops an arborification map on decorated trees to compute cancellations in random-data dispersive PDEs, enabling results on wave turbulence and 3D cubic wave equation Gibbs measure invariance.
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Stochastic estimates for the thin-film equation with thermal noise
Constructs uniform estimates and explicit counterterm for the renormalized stochastic thin-film equation in the full subcritical regime across dimensions d ≥ 1.