Content:

• Preliminaries on Random Variables (limit theorems, classical inequalities, Gaussian models, Monte Carlo)
• Concentrations of Sums of Independent Random Variables
• Random Vectors in High Dimensions
• Random Matrices
• Concentration for variables with dependency
• Geometric examples of concentration
• Suprema of random processes and fields

Books:

We will follow the 23/24 lecture notes of Dr Stefan Adams. Themselves these are drawn largely from the recent texts

[1] Roman Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics, (2018).

[2] Martin Wainwright, High dimensional Statistics: A non-asymptotic viewpoint. CUP, 2019.