Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA Bo‘az Klartag,Emanuel Milman Book 2020 Springer Nature Switzerland AG 2020 A

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,Gromov’s Waist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures,lanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian measures. In the other appendix, we provide a comparison of different variations of Gromov’s pancake method.

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,Gromov’s Waist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures,st of radially symmetric Gaussian measures. In particular, it turns out possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no .-neighborhood waist property, including a rather wide class of compa

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,On the Poincaré Constant of Log-Concave Measures,e revisit E. Milman’s result (Invent Math 177:1–43, 2009) on the link between weak (Poincaré or concentration) inequalities and Cheeger’s inequality in the log-concave cases, in particular extending localization ideas and a result of Latala, as well as providing a simpler proof of the nice Poincaré

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Information and Dimensionality of Anisotropic Random Geometric Graphs,om geometric graph in which vertices correspond to points generated randomly and independently from a non-isotropic .-dimensional Gaussian distribution, and two vertices are connected if the distance between them is smaller than some pre-specified threshold. We derive new notions of dimensionality w