A large deviations principle is established for rogue waves in the cubic nonlinear Schrödinger equation with randomized quasi-periodic initial data in dimensions d>1, holding for times O(ε^{-1-η}) under polynomial Fourier decay.
Bourgain, Periodic nonlinear S chr\" o dinger equation and invariant measures, Comm
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Large Deviations for the Nonlinear Schrodinger Equation with Randomized Quasi-Periodic Initial Data in Higher Dimensions: Beyond the Critical Time Scale
A large deviations principle is established for rogue waves in the cubic nonlinear Schrödinger equation with randomized quasi-periodic initial data in dimensions d>1, holding for times O(ε^{-1-η}) under polynomial Fourier decay.