All Questions
Tagged with eigenvector pr.probability
9 questions
1
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80
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Inequality involving random vectors and absolute values
Let $\mathbb{X}, \mathbb{Y} \subset \mathbb{R}^d$ be finite sets. Suppose random vectors $X \in \mathbb{X}$ and $Y \in \mathbb{Y}$ are sampled according to a joint distribution $\mathbb{P}_{XY}$. ...
1
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1
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84
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Asymptotic property of the left singular vectors of i.i.d. data matrix
Let $\mathbf{X}$ be $(n \times p)$-dimensional data matrix ($n > p$) whose rows $\mathbf{x}_i$ are i.i.d. with some finite moments:
$$
\mathbf{X}^\top = [\mathbf{x}_1, \ldots \mathbf{x}_n]^\top.
...
- 284
1
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66
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CLT of the left singular vectors of i.i.d. data matrix
Let $\mathbf{X}$ be $(n \times p)$-dimensional random matrix ($n > p$) whose rows $\mathbf{x}_i$ are i.i.d. with some finite moments:
$$
\mathbf{X}^\top = [\mathbf{x}_1, \ldots \mathbf{x}_n]^\...
- 284
13
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1
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697
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$\ell^1$-norm of eigenvectors of Erdős-Renyi Graphs
Setting. Let $G(n,p)$ denote the usual Erdős-Renyi (random) graphs. For each such graph there is an associated Laplacian matrix $L = D - A$ where $D$ collects the degrees on the diagonal and $A$ is ...
2
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1
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704
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Distribution of eigenvectors of random matrices and link with the components of the matrix
Let $M$ be a real symmetric matrix of size $N$ with its components $M_{ij}$ following a normal distribution centered around 0.
Let $x\in\mathbb{R}^N$ be an eigenvector of $M$ with eigenvalue $\lambda\...
- 117
4
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0
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463
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The distribution of the elements of an eigenvector of random matrices
Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from ...
- 39
3
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1
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247
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Concentration and Correlation for Magnitudes of Gaussian Vectors
Suppose we have a large collection of standard normal random variables $a_i\in\mathbb{R}^n$. We know by standard concentration results that if we take $m \geq C\left(t/\epsilon\right)^2n$ samples, ...
- 205
1
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147
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Bounding Rayleigh quotient for stochastic matrix
Suppose you have an irreducible, stochastic matrix $A$ with left Perron-Frobenius eigenvector $v$ (corresponding to the eigenvalue $1$), and suppose the next largest eigenvalue for $A$ is $\lambda$. ...
- 121
1
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1
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160
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Optimum control of a probabilistic automaton
Suppose we have a probabilistic automaton and we assign a weight to each state. An "interaction strategy" would be a fixed map from states to inputs. Any interaction strategy could be used to ...
