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We extend a randomisation method, introduced by Shiffman-Zelditch and developed by Burq-Lebeau on compact manifolds for the Laplace operator, to the case of $\mathbb{R}^d$ with the harmonic oscillator.
On Equivalence of Infinite Product Measures
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Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity
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Ann. Sci. Éc. Norm. Supér
N. Burq and G. Lebeau. Injections de Sobolev probabilistes et applications
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Solutions globales pour des équations de Schrödinger sur-critiques en toutes dimensions
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Random weighted Sobolev inequalities and application to quantum ergodicity. Preprint. hal-00919443
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Semiclassical L p L^{p} Estimates
H. Koch, D. Tataru and M. Zworski · 2007
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Random data Cauchy theory for supercritical wave equations I: local existence theory
N. Burq and N. Tzvetkov · 2008
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Random data Cauchy theory for supercritical wave equations II: A global existence result
N. Burq and N. Tzvetkov · 2008
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N. Burq and N. Tzvetkov · 2011
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Median and mean of the Supremum of L 2 L^{2} normalized random holomorphic fields
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R. Feng and S. Zelditch · 2013
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