Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications

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New Berry-Esseen bounds for non-linear functionals of Poisson random measures (2013, background): “Applications of findings dealing with the Gaussian case have found notable applications in the theory and statistics of Gaussian random processes [3, 4] (most prominently the fractional Brownian motion [16]), spherical random fields [1, 15], random matrix theory [18] and universality questions [20],”
Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on S^d (2014, unknown): “subordi-nated random ﬁelds In this section, we ﬁrst brieﬂy review some notation and the main results in this area, which we shall deeply exploit in the sequel of the paper.”
The optimal fourth moment theorem (2013, unknown): “MSC 2010: 60F05; 60G15; 60H07”
A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions (2016, background): “Finally, we recall that the spherical harmonic coefficients satisfy the identities (−1)ma ,−m = ā m ([17], formula (6.”
Excursion probability of Gaussian random fields on sphere (2014, methodology): “(1)<∞ is equivalent to P∞ n=0 n N−2a n <∞. When N =2 and λ=1/2, Pλ n (n≥0) become the Legendre polynomials. For more results on isotropic Gaussian ﬁelds on S2, we refer to Marinucci and Peccati [25]. Regularity and smoothness properties of Gaussian ﬁeld {X(x): x∈S2} have recently been obtained”