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Results tagged with random-matrices
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user 11054
Statistics of spectral properties of matrix-valued random variables.
2
votes
stationary measure for linear cocycle(random transformation matrices)
If $A_1=\begin{pmatrix}1&0\\1&1\end{pmatrix}$ and $A_2=\begin{pmatrix}1&1\\0&1\end{pmatrix}$, and the measure on $\{A_1,A_2\}^{\mathbb Z}$ is the $(\frac 12,\frac 12)$ Bernoulli measure, then there is …
- 23.2k
7
votes
Accepted
Asymptotic behavior of the ratio between the largest two singular values of product of i.i.d...
So this is correct. The theorem that you need is the multiplicative ergodic theorem. Expressing it in your language, it states that $\frac 1n\log s_i(A_n)\to\lambda_i$, where $s_i$ is the $i$th singul …
- 23.2k
5
votes
Accepted
Lyapunov exponents of dual / adjoint / transpose random dynamical system (RDS)
The theory is right! If $H_i$ has negative Lyapunov exponents, then images of any vector under the transpose system will be exponentially close to a single vector (everything is being compressed in th …
- 23.2k
3
votes
Determine the expected size of a lower triangular sub-matrix of a random matrix?
A reasonable first estimate is $\ell$ (the size of $L$) is approximately $4\log n/|\log p|$.
To get this, consider choosing a sequence of $k$ rows $i_1,\ldots,i_k$ and $k$ columns, $j_1,\ldots j_k$. …
- 23.2k
10
votes
Probability that a random distance function is metric
Since you haven't given a distribution, let me make an observation giving the right form of the answer in the case where the $D_{xy}$ are independent uniform $[0,1]$ random variables.
I want to clai …
- 23.2k