Smallest singular value of sparse random matrices

Alexander E. Litvak, and Omar Rivasplata. "Smallest singular value of sparse random matrices." Studia Mathematica 212.3 (2012): 195-218. <http://eudml.org/doc/285374>.

@article{AlexanderE2012,
abstract = {We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances of the entries. We also show that it is enough to require boundedness from above of the rth moment, r > 2, of the corresponding entries.},
author = {Alexander E. Litvak, Omar Rivasplata},
journal = {Studia Mathematica},
keywords = {random matrices; sparse matrices; singular values; deviation inequalities},
language = {eng},
number = {3},
pages = {195-218},
title = {Smallest singular value of sparse random matrices},
url = {http://eudml.org/doc/285374},
volume = {212},
year = {2012},
}

TY - JOUR
AU - Alexander E. Litvak
AU - Omar Rivasplata
TI - Smallest singular value of sparse random matrices
JO - Studia Mathematica
PY - 2012
VL - 212
IS - 3
SP - 195
EP - 218
AB - We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances of the entries. We also show that it is enough to require boundedness from above of the rth moment, r > 2, of the corresponding entries.
LA - eng
KW - random matrices; sparse matrices; singular values; deviation inequalities
UR - http://eudml.org/doc/285374
ER -