Abstract
In this article we first review some by-now classical results about the geometry of ℓ p-balls \(\mathbb {B}_p^n\) in \(\mathbb {R}^n\) and provide modern probabilistic arguments for them. We also present some more recent developments including a central limit theorem and a large deviations principle for the q-norm of a random point in \(\mathbb {B}_p^n\). We discuss their relation to the classical results and give hints to various extensions that are available in the existing literature.
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Prochno, J., Thäle, C., Turchi, N. (2019). Geometry of \(\ell _p^n\,\text{-Balls}\): Classical Results and Recent Developments. In: Gozlan, N., Latała, R., Lounici, K., Madiman, M. (eds) High Dimensional Probability VIII. Progress in Probability, vol 74. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-26391-1_9
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