# the MIC Seminar

The Mathematics, Information and Computation (MIC) Seminar runs at irregular intervals and covers specific aspects at the interface of applied maths, information theory and theory of computation.

### Schedule Spring 17

Date & Time | Speaker | Title | Room |
---|---|---|---|

Mar 21, 2:30pm | Liza Rebrova (U Michigan) | Local and global obstructions for the random matrix norm regularization | CDS 650 |

### Abstracts

#### Liza Rebrova: Local and Global obstructions for the random matrix norm regularization

We study large n by n random matrices A with i.i.d. entries. If the distribution of the entries have mean zero and at least gaussian decay, then the operator norm ||A|| is at most of order sqrt(n) with high probability. However, for the distributions with heavier tails we cannot expect the same norm bound any more. So, we are motivated by the question: under what conditions operator norm of a heavy-tailed matrix can be improved by modifying just a small fraction of its entries (a small sub-matrix of A)? I will explain why this happens exactly when the entries of A have zero mean and bounded variance. I will also discuss the almost optimal dependence between the size of the removed sub-matrix and the resulting operator norm that we’ve obtained. This is a joint work with Roman Vershynin, inspired by the methods developed recently by Can Le and R. Vershynin and in our joint work with Konstantin Tikhomirov.
**Room:** Center for Data Science, NYU, 60 5th ave, room 650
**Time:** 2:30pm-3:30pm.