Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2008 | public
Journal Article Open

The random paving property for uniformly bounded matrices

Tropp, Joel A.


This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of Bourgain and Tzafriri involves a long, delicate calculation. The new proof relies on the systematic use of symmetrization and (noncommutative) Khinchin inequalities to estimate the norms of some random matrices.

Additional Information

This work was supported by NSF DMS 0503299. I wish to thank Roman Vershynin for encouraging me to study the paving problem.

Attached Files

Submitted - 0612070


Files (201.6 kB)
Name Size Download all
201.6 kB Download

Additional details

August 19, 2023
August 19, 2023