M. V. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A Math. Gen. 10 (1977), no. 12, 2083–2091. MR489542
M. V. Berry, Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature, J. Phys. A Math. Gen. 35 (2002), no. 13, 3025–3038. MR1913853
J. M. Borwein, D. Nuyens, A. Straub, and J. Wan, Some arithmetic properties of short random walk integrals, Ramanujan J. 26 (2011), no. 1, 109–132. MR2837721
J. M. Borwein, A. Straub, and C. Vignat, Densities of short uniform random walks in higher dimensions, J. Math. Anal. Appl. 437 (2016), no. 1, 668–707. MR3451989
J. M. Borwein, A. Straub, and J. Wan, Three-step and four-step random walk integrals, Exp. Math. 22 (2013), no. 1, 1–14. MR3038778
J. M. Borwein, A. Straub, J. Wan, and W. Zudilin, Densities of short uniform random walks, Canad. J. Math. 64 (2012), no. 5, 961–990, With an appendix by Don Zagier. MR2979573
P. Breuer and P. Major, Central limit theorems for nonlinear functionals of Gaussian fields, J. Multivariate Anal. 13 (1983), no. 3, 425–441. MR716933
S. Cohen and M. A. Lifshits, Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres, ESAIM Probab. Stat. 16 (2012), 165–221. MR2946126
F. Grotto and G. Peccati, Nonlinear Functionals of Hyperbolic Random Waves: the Wiener Chaos Approach, arXiv e-prints (2023), arXiv:2301.08315.
J. C. Kluyver, Some formulae concerning the integers less than n and prime to n, Koninklijke Nederlandse Akademie van Wetenschappen Proceedings Series B Physical Sciences 9 (1906), 408–414.
I. Krasikov, Approximations for the Bessel and Airy functions with an explicit error term, LMS J. Comput. Math. 17 (2014), no. 1, 209–225. MR3230865
L. Maini, Asymptotic covariances for functionals of weakly stationary random fields, Stochastic Process. Appl. 170 (2024), Paper no. 104297. MR4689941
L. Maini and I. Nourdin, Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields, Ann. Probab., in press (2024+), arXiv:2206.14458.
D. Marinucci and G. Peccati, High-frequency asymptotics for subordinated stationary fields on an abelian compact group, Stochastic Process. Appl. 118 (2008), no. 4, 585–613. MR2394764
D. Marinucci and G. Peccati, Group representations and high-resolution central limit theorems for subordinated spherical random fields, Bernoulli 16 (2010), no. 3, 798–824. MR2730649
D. Marinucci and G. Peccati, Random fields on the sphere, London Mathematical Society Lecture Note Series, vol. 389, Cambridge University Press, Cambridge, 2011, Representation, limit theorems and cosmological applications. MR2840154
D. Marinucci and M. Rossi, Stein-Malliavin approximations for nonlinear functionals of random eigenfunctions on Sd, J. Funct. Anal. 268 (2015), no. 8, 2379–2420. MR3318653
D. Marinucci and I. Wigman, The defect variance of random spherical harmonics, J. Phys. A Math. Theor. 44 (2011), no. 35, 355206.
D. Marinucci and I. Wigman, On nonlinear functionals of random spherical eigenfunctions, Commun. Math. Phys. 327 (2014), no. 3, 849–872. MR3192051
M. Notarnicola, Probabilistic limit theorems and the geometry of random fields, Ph.D. thesis, Luxembourg University, 2021. MR4678940
I. Nourdin and G. Peccati, Normal approximations with Malliavin calculus, Cambridge Tracts in Mathematics, vol. 192, Cambridge University Press, Cambridge, 2012, From Stein’s method to universality. MR2962301
I. Nourdin, G. Peccati, and M. Rossi, Nodal statistics of planar random waves, Comm. Math. Phys. 369 (2019), no. 1, 99–151. MR3959555
K. Pearson, The problem of the random walk, Nature 72 (1905), no. 1865, 294–294.
M. Rossi, The defect of random hyperspherical harmonics, J. Theoret. Probab. 32 (2019), no. 4, 2135–2165. MR4020703
G. Szego, Orthogonal polynomials, American Math. Soc: Colloquium publ, American Mathematical Society, 1939. MR0000077
A. P. Todino, A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2, J. Math. Phys. 60 (2019), no. 2, 023505, 33. MR3916834
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Li-brary, Cambridge University Press, Cambridge, 1995, Reprint of the second (1944) edition. MR1349110
I. Wigman, Fluctuations of the nodal length of random spherical harmonics, Comm. Math. Phys. 298 (2010), no. 3, 787–831. MR2670928
Igor Wigman, On the nodal structures of random fields: a decade of results, Journal of Applied and Computational Topology (2023), 1–43.
S. Zelditch, Real and complex zeros of Riemannian random waves, Spectral analysis in geometry and number theory, Contemp. Math., vol. 484, Amer. Math. Soc., Providence, RI, 2009, pp. 321–342. MR1500155