]. N. Ana16 and . Anantharaman, Topologie des hypersurfaces nodales de fonctions aléatoires gaussiennes, Séminaire Bourbaki, vol.68, pp.2015-2016, 1116.

J. Angst, G. Poly, and V. Pham, Universality of the nodal length of bivariate random trigonometric polynomials Accepted in Trans AMS Arxiv preprint : https://arxiv L p properties for Gaussian random series, Trans. Amer. Math. Soc, issue.8, pp.3604425-4439, 2008.

M. Berger, P. Gauduchon, and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, vol.194, 1971.
DOI : 10.1007/bfb0064646

N. Burq, P. Gérard, N. Tzvetkov, and G. Lebeau, Injections de Sobolev probabilistes et applications Brezis and L. Nirenberg. Degree theory and BMO; part I: Compact manifolds without boundaries On the characterization of pseudodifferential operators (old and new) In Studies in Phase Space Analysis with Applications to PDEs The Schrödinger Equation, Selecta Mathematica, New Series Semi-classical calculus on manifolds with ends and weighted L p estimates. Ann. Inst. FourierBT08] N. Burq and N. Tzvetkov. Random data Cauchy theory for supercritical wave equations I: local theory. Inventiones mathematicae Tzvetkov. Probabilistic well-posedness for the cubic wave equation, pp.569-605917, 1074.
DOI : 10.24033/asens.2206

URL : http://arxiv.org/abs/1111.7310

J. [. Dimassi, A. Sjöstrand, ]. F. De-suzzonifm10, H. N. Filbir, and . Mhaskar, Spectral asymptotics in the semi-classical limit Consequences of the choice of a particular basis of L 2 (S 3 ) for the cubic wave equation on the sphere and the Euclidian space A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel [Hör68] L. Hörmander. The spectral function of an elliptic operator The analysis of linear partial differential operators vol III : Pseudo-differential operators, Hör85] L. HörmanderHR81] B. Helffer and D. Robert. Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques, pp.991-1015629, 1968.

A. Inst, . Fourierhr82-]-b, D. Helffer, and . Robert, Proprietes asymptotiques du spectre d operateurs pseudo-differentiels sur Rn, HZ11] H. Hofer and E. Zehnder. Symplectic invariants and Hamiltonian dynamics, pp.31169-223795, 1981.

B. Hanin, S. Zelditch, P. Zhouime17, ]. Imekraz, D. Robert et al., Nodal sets of random eigenfunctions for the isotropic harmonic oscillator Concentration et randomisation universelle de sous-espaces propres Accepted in Analysis & PDE, HAL preprint https://hal.archives-ouvertes.fr/hal-01564960/document On random Hermite series Integrability of infinite sums of independent vector-valued random variables, JN61] F. John and L. Nirenberg. On functions of bounded mean oscillation. Comm. Pure Appl, pp.20154813-48392763, 1961.

J. E. Karadzhov, Riesz summability of multiple Hermite series inL p spaces, Koch and D. Tataru. L p eigenfunction bounds for the Hermite operator, pp.107-118369, 1968.
DOI : 10.1007/BF02572353

H. Koch, D. Tataru, M. Zworskiler10-]-n, . Lerner-[-lq04-]-d, H. Li et al., Semiclassical Lp Estimates, Probability in Banach Spaces: isoperimetry and processes Pisier. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach Marcus and G. Pisier. Random Fourier Series with Applications to Harmonic Analysis. Annals of Math Studies, pp.885-91645, 1976.
DOI : 10.1007/s00023-006-0324-2

URL : http://arxiv.org/abs/math-ph/0603080

B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. I, Transactions of the American Mathematical Society, vol.147, issue.2, pp.433-460, 1970.
DOI : 10.1090/S0002-9947-1970-99933-9

A. Poiret, D. Robert, and L. Thomann, Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator, Analysis & PDE, vol.42, issue.4, pp.997-1026, 2014.
DOI : 10.1007/3-540-45276-1

URL : https://hal.archives-ouvertes.fr/hal-00857679

A. Poiret, D. Robert, L. H. Thomann-ann, A. Poincaré, . Math et al., Random weighted Sobolev inequalities on R d and applications to Hermite functions On some series of functions, Proc. Camb, pp.651-689, 1930.

L. [. Robert, . [. Thomann, C. Robbiano, . Zuilysle81-]-w, ]. T. Sleddtv10 et al., Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials Random series which are BMO or Theory of function spaces Random matrices: The distribution of the smallest singular values, Tao12] T. Tao. Topics in random matrix theory, pp.1181-1209718, 1981.

G. [. Yajima, G. Zhang, and . Zhang, Smoothing property for Schrödinger equations with Potential Superquadratic at Infinity Local smoothing property and Strichartz inequality for Schrödinger operator with potentials superquadratic at infinity, Zel09] S. Zelditch. Real and complex zeros of Riemannian random waves. Contemporary Mathematics, pp.573-59081, 2001.
DOI : 10.1007/s002200100483