TY - JOUR

T1 - The smallest singular value of random rectangular matrices with no moment assumptions on entries

AU - Tikhomirov, Konstantin E.

N1 - Publisher Copyright:
© 2016, Hebrew University of Jerusalem.

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, N0 depending only on β and δ with the following property: for any N,n such that N ≥ max(N0, δn), any N × n random matrix A = (aij) with i.i.d. entries satisfying (Formula presented.) and any non-random N × n matrix B, the smallest singular value sn 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, N0 depending only on β and δ with the following property: for any N,n such that N ≥ max(N0, δn), any N × n random matrix A = (aij) with i.i.d. entries satisfying (Formula presented.) and any non-random N × n matrix B, the smallest singular value sn 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 -