Roman Vershynin studies high-dimensional probability theory and its applications to data. His High-Dimensional Probability by Roman Vershynin develops tools including concentration inequalities, random-matrix estimates and generic chaining, which turn geometry and independence into bounds that hold simultaneously over many directions.[ref]
High-Dimensional Probability by Roman Vershynin. First edition, random matrices and Chapter 8, chaining
A representative question is how many random observations are needed to preserve information about a high-dimensional object. Controlling one fixed direction is easier than controlling every direction at once, so the geometry of a whole family of directions becomes part of the probability calculation. His research page describes this connection between probability and mathematical data science; his author-hosted expository work also treats geometric methods for constrained estimation.[ref][ref]
https://arxiv.org/abs/1405.5103. Author's Estimation in high dimensions: a geometric perspective, abstract
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