Abstract
AbstractFor $$m,n\in \mathbb {N}$$
m
,
n
∈
N
, let $$X=(X_{ij})_{i\le m,j\le n}$$
X
=
(
X
ij
)
i
≤
m
,
j
≤
n
be a random matrix, $$A=(a_{ij})_{i\le m,j\le n}$$
A
=
(
a
ij
)
i
≤
m
,
j
≤
n
a real deterministic matrix, and $$X_A=(a_{ij}X_{ij})_{i\le m,j\le n}$$
X
A
=
(
a
ij
X
ij
)
i
≤
m
,
j
≤
n
the corresponding structured random matrix. We study the expected operator norm of $$X_A$$
X
A
considered as a random operator between $$\ell _p^n$$
ℓ
p
n
and $$\ell _q^m$$
ℓ
q
m
for $$1\le p,q \le \infty $$
1
≤
p
,
q
≤
∞
. We prove optimal bounds up to logarithmic terms when the underlying random matrix X has i.i.d. Gaussian entries, independent mean-zero bounded entries, or independent mean-zero $$\psi _r$$
ψ
r
($$r\in (0,2]$$
r
∈
(
0
,
2
]
) entries. In certain cases, we determine the precise order of the expected norm up to constants. Our results are expressed through a sum of operator norms of Hadamard products $$A\circ A$$
A
∘
A
and $$(A\circ A)^T$$
(
A
∘
A
)
T
.
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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