4 papers · 1 filter
Random processes via the combinatorial dimension: introductory notes
Mark Rudelson, Roman Vershynin
This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of conve…
Coordinate restrictions of linear operators in
R. Vershynin
This paper addresses the problem of improving properties of a linear operator u in by restricting it onto coordinate subspaces. We discuss how to reduce the norm of u by a…
John decompositions: selecting a large part
R. Vershynin
We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositions id = \sum x_j \otimes x_j, rather than on the coordinate one. T…
Subsequences of frames
R. Vershynin
Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - ε) n. On the other hand, th…