Back to Search Start Over

Norms of random matrices: Local and global problems

Authors :
Rebrova, E
Rebrova, E
Vershynin, R
Rebrova, E
Rebrova, E
Vershynin, R
Publication Year :
2018

Abstract

Can the behavior of a random matrix be improved by modifying a small fraction of its entries? Consider a random matrix A with i.i.d. entries. We show that the operator norm of A can be reduced to the optimal order O(n) by zeroing out a small submatrix of A if and only if the entries have zero mean and finite variance. Moreover, we obtain an almost optimal dependence between the size of the removed submatrix and the resulting operator norm. Our approach utilizes the cut norm and Grothendieck–Pietsch factorization for matrices, and it combines the methods developed recently by C. Le and R. Vershynin and by E. Rebrova and K. Tikhomirov.

Details

Database :
OAIster
Notes :
application/pdf
Publication Type :
Electronic Resource
Accession number :
edsoai.on1287326150
Document Type :
Electronic Resource