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High-Dimensional Probability (Vershynin)
High-Dimensional Probability (Vershynin)
1 questions
Difficulty 10-10
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advanced (10/10)
state theorem
The Marchenko-Pastur law describes the limiting eigenvalue distribution of sample covariance matrices
Σ
^
=
n
1
X
T
X
when
X
has i.i.d. entries. What setup gives non-trivial eigenvalue support?
Hide and think first
A.
X
with IID entries drawn from a specific heavy-tailed distribution, not Gaussian
B.
X
∈
R
n
×
1
with
n
→
∞
and
d
=
1
fixed (classical case)
C.
X
∈
R
n
×
d
with
n
,
d
→
∞
and
d
/
n
→
c
>
0
(comparable dimensions)
D.
X
=
A
B
where
A
and
B
are deterministic, with
X
having no random structure
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