TY - JOUR
T1 - The smallest singular value of random rectangular matrices with no moment assumptions on entries
AU - Tikhomirov, Konstantin
PY - 2016/5/1
Y1 - 2016/5/1
N2 -
Let δ > 1 and β > 0 be some real numbers. We prove that there are positive u, v, N
0
depending only on β and δ with the following property: for any N,n such that N ≥ max(N
0
, δ
n
), any N × n random matrix A = (a
ij
) with i.i.d. entries satisfying (Formula presented.) and any non-random N × n matrix B, the smallest singular value s
n
of A + B satisfies (Formula presented.). The result holds without any moment assumptions on the distribution of the entries of A.
AB -
Let δ > 1 and β > 0 be some real numbers. We prove that there are positive u, v, N
0
depending only on β and δ with the following property: for any N,n such that N ≥ max(N
0
, δ
n
), any N × n random matrix A = (a
ij
) with i.i.d. entries satisfying (Formula presented.) and any non-random N × n matrix B, the smallest singular value s
n
of A + B satisfies (Formula presented.). The result holds without any moment assumptions on the distribution of the entries of A.
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U2 - 10.1007/s11856-016-1287-8
DO - 10.1007/s11856-016-1287-8
M3 - Article
AN - SCOPUS:84953400050
SN - 0021-2172
VL - 212
SP - 289
EP - 314
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -