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user 113397
10
votes
Accepted
Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
From the identities in @OlivierBégassat's answer, the inequality $\Bbb E\det X^2\ge\det\Bbb EX^2$ can be written as $$\small n!\sum_{f=0}^n\binom nf(-1)^{n-f-1}(n-f-1)(\Bbb V[X]+\Bbb E[X]^2)^f\Bbb E[X …
- 1,459
8
votes
3
answers
585
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Jensen-like inequality for random matrix: $\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$
Let $X\in M_n(\Bbb R)$ be a random matrix with iid elements following a continuous distribution.
What are the necessary and sufficient conditions for $$\Bbb E[\det X^2]\ge\det\Bbb E[X^2]$$ to hold? Is …
- 1,459