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Results tagged with random-matrices
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user 48831
Statistics of spectral properties of matrix-valued random variables.
6
votes
Expected determinant of random symmetric matrix with different Gaussian distributions of the...
Here is a another approach.
For convenience I write $n$ instead of $N$, and $A_n$ for $A$.
By definition
$$\det(A_n) = \sum_{\pi\in S_n} \operatorname{sign}(\pi) \prod_{i=1}^n a_{i,\pi(i)}$$
By …
- 3,255
1
vote
Accepted
Expected value of a function over random sets
I assume you mean picking a random $k$-subset from {1,...,n}, i.e. drawing without
replacement? In this case one finds for $X_j=\alpha_j-j$ that
$$\mathbb{E}(t^{X_j})= {k!\,(n-k)! \over n!} [x^{n-k}] …
- 3,255