K. Driver and K. Jordaan. Bounds for extreme zeros of some classical orthogonal polynomials. Journal of Approximation Theory, 164(9):1200-1204, 2012. ISSN 0021-9045. doi: https://doi.org/10.1016/j.jat.2012.05.014. URL https://www.sciencedirect.com/science/article/pii/S0021904512001050.
Rishabh Dudeja and Daniel Hsu. Learning single-index models in gaussian space. In Sébastien Bubeck, Vianney Perchet, and Philippe Rigollet, editors, Proceedings of the 31st Conference On Learning Theory, volume 75 of Proceedings of Machine Learning Research, pages 1887-1930. PMLR, 06-09 Jul 2018. URL https://proceedings.mlr.press/v75/dudeja18a.html.
David A Freedman. On tail probabilities for martingales. the Annals of Probability, pages 100-118, 1975.
Spencer Frei, Yuan Cao, and Quanquan Gu. Agnostic learning of a single neuron with gradient descent. Advances in Neural Information Processing Systems, 33:5417-5428, 2020.
Christopher Frye and Costas J Efthimiou. Spherical harmonics in p dimensions. arXiv preprint arXiv:1205.3548, 2012.
Walter Gautschi. Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys, 38(1):77-81, 1959.
Surbhi Goel, Aravind Gollakota, Zhihan Jin, Sushrut Karmalkar, and Adam Klivans. Superpolynomial lower bounds for learning one-layer neural networks using gradient descent. In International Conference on Machine Learning, pages 3587-3596. PMLR, 2020.
Sham M Kakade, Varun Kanade, Ohad Shamir, and Adam Kalai. Efficient learning of generalized linear and single index models with isotonic regression. Advances in Neural Information Processing Systems, 24, 2011.
Adam Tauman Kalai and Ravi Sastry. The isotron algorithm: High-dimensional isotonic regression. In  $COLT$ , 2009.
Boaz Klartag. A central limit theorem for convex sets. Inventiones mathematicae, 168(1):91-131, 2007.
Andrea Laforgia and Pierpaolo Natalini. On some inequalities for the gamma function. Advances in Dynamical Systems and Applications, 8(2):261-267, 2013.
Jonathan Niles-Weed and Philippe Rigollet. Estimation of Wasserstein distances in the spiked transport model. Bernoulli, 28(4):2663-2688, 2022.
François-Pierre Paty and Marco Cuturi. Subspace robust Wasserstein distances. In International conference on machine learning, pages 5072-5081. PMLR, 2019.
Adrian Röllin. Stein's method in high dimensions with applications. In Annales de l'IHP Probabilités et statistiques, volume 49, pages 529-549, 2013.
Shai Shalev-Shwartz, Ohad Shamir, and Karthik Sridharan. Learning kernel-based halfspaces with the zero-one loss. arXiv preprint arXiv:1005.3681, 2010.
Ohad Shamir. Distribution-specific hardness of learning neural networks. The Journal of Machine Learning Research, 19(1):1135-1163, 2018.
Mahdi Soltanolkotabi. Learning relus via gradient descent. Advances in neural information processing systems, 30, 2017.
Min Jae Song, Ilias Zadik, and Joan Bruna. On the cryptographic hardness of learning single periodic neurons. Advances in Neural Processing Systems (NeurIPS), 2021.
Adriaan J Stam. Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces. Journal of Applied probability, 19(1):221-228, 1982.
Gabor Szego. Orthogonal polynomials, volume 23. American Mathematical Soc., 1939.