4 papers
math.PR2026
Two friendly proofs of the Berry-Esseen theorem
Roman Vershynin
A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of two dif…
math.CO2024
Are most Boolean functions determined by low frequencies?
Roman Vershynin
We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function there exists a funct…
cs.CG2007
Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms
Roman Vershynin
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- comput…
math.FA1998
Absolutely representing systems, uniform smoothness, and type
R. Vershynin
Absolutely representing system (ARS) in a Banach space is a set such that every vector in admits a representation by an absolutely convergent series $x =…