# Tagged Questions

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### What background is required to understand Random Matrix Theory

I would like to be able to understand RMT but after "reading" many articles I have found that I have a limited capacity. I just see complicated equations. I guess I know linear algebra, classical ...
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Let $(\mathbb{R}^k,{\cal A})$ be a measurable space. Fix $c>0$ and for every $X\in \mathbb{R}^k$ define $X_c$ as $k-$dimensional vector such that the $i-th$ element of $X^{(c)}$ is $(-c)\vee ... 1answer 204 views ### Sum of Wishart matrices Considering two matrices,$H_1$and$H_2$, that are independent of each other and follows complex wishart distributions as$\mathcal{CW} _m(n_1,\Sigma_1)$and$\mathcal{CW} _m(n_2,\Sigma_2)$... 1answer 97 views ### If a sequence of random matrices converge in probability, do their elements also converge? Is it true that if a sequence of random matrices$\{X_n\}$converge in probability to a random matrix$X_n\overset{P}{\to}X$as$n\to\infty$that the elements$X_n^{(i,j)}\overset{P}{\to} X^{(i,j)}$... 1answer 46 views ### Question regard the notion of almost sure convergence Consider an$n\times m$matrix with i.i.d. entries each having zero mean and variance$1/n$. Let$Y = X^TX$. By the strong law of large numbers, we know that the$(i,j)$entry of$Y$goes almost ... 1answer 70 views ### Random Matrix Question Let$A$be a$n\times m$($n<m$) random matrix with normal i.i.d. entries ($N(0,1)$). Using the law of large numbers, it readily can be shown that as$n\to\infty$$$\frac{1}{n}A^TA\to I_m$$ ... 0answers 72 views ### trace class norms of random matrices We denote by$||.||_1$the trace class norm. on$M_n$.Let$(r_{ij})_{1 \leq i,j\leq n}$be a family of independent identically distributed random variables which take the values$-1$and$1$with ... 1answer 369 views ### Expected value of a multivariate distribution Given this random vector: $$\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$$ And this probability distribution function that takes it as argument:$$f_\mathbf{X}(\mathbf{x}) = ... 1answer 118 views ### Is Wishart Matrix? Analyzing a system, I have faced a problem which is related to Random Matrices and in particular Wishart matrix. The problem is as follows: Lets assume$\boldsymbol{H}$is an$m\times n$random ... 0answers 56 views ### How to determine the degrees of freedom of an inner-product matrix of two random matrices? I have two random matrices A and B, with N columns each. The columns of A and B are independent but not necessarily identically distributed. A and B may be considered as two instances of an underlying ... 0answers 65 views ### Suboptimal confidence for bounds on the extreme eigenvalues of random matrices: can they be improved? Typical results from the literature of Random Matrix Theory (RMT) (e.g., Tropp'11, Vershynin'12) provide probabilistic guarantees for large deviation of the extreme eigenvalues of random matrices like ... 0answers 274 views ### Slutsky's theorem for random matrices This image is from Applied Multivariate Analysis. In this image plim means convergence in probability. I could not find the reference about the statement for ... 1answer 482 views ### spectral norm of random matrix Suppose$A$is a$n \times n$random matrix with centered Gaussian (real) i.i.d entries with variance$\sigma^2/n$. What to we know about the spectral norm$s(A)$of$A$, that is$\sqrt{\rho(A^t A)}$... 0answers 82 views ### Studying the maxima of columns of a random matrix as a point process Consider a matrix,$S$, of i.i.d. real RVs :$X_{ij}$for$1 \leq i \leq s$,$1 \leq j \leq n$. Let$F$denote the distribution of$X_{ij}$. For$1 \leq j \leq n$, consider$Y_{j}^{(1)} = \max_{i} ...
Lets generate a random symmetric matrix $A$ by generating the entries of a random matrix $Z$ iid from some continuous distribution, and setting $A=(1/2)(Z+Z^T)$. I think its true that $A$ should have ...