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Every Spring starting Sp 2021
The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional probability.
At the level of R. Vershynin, High-Dimensional Probability. An Introduction with Applications in Data Science, Cambridge University Press, 2018.
- Concentration inequalities : Bernstein-type, the Hanson-Wright inequality, Talagrand's inequality for product measures, concentration on the Gaussian measure space.
- Gaussian processes: Slepian's, Sudakov's inequalities; Dudley's and Talagrand's chaining.
- Non-asymptotic random matrix theory: the condition number of Gaussian matrices, elements of the Littlewood-Offord theory, compressed sensing and the Restricted Isometry Property, applications of the resolvent method and the trace method.