In this article we first review some by-now classical results about the geometry of ℓp-balls in 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 We discuss their relation to the classical results and give hints to various extensions that are available in the existing literature.
Prochno, J., Thäle, C., Turchi, N. (2019). Geometry of lp-Balls: Classical Results and Recent Developments. In N. Gozlan, R. Latała, K. Lounici, M. Madiman (a cura di), High Dimensional Probability VIII. The Oaxaca Volume (pp. 121-150). Birkhäuser [10.1007/978-3-030-26391-1_9].
Geometry of lp-Balls: Classical Results and Recent Developments
Turchi, N
2019
Abstract
In this article we first review some by-now classical results about the geometry of ℓp-balls in 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 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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