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Results tagged with pr.probability
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user 62673
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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"Probability" for a partitioned matrix to be singular
Let $A,B\in\mathbb{R}^{n\times n}$ be two nonsingular matrices with $A\ne B$, and consider the following partitioned matrix
$$
M:=\begin{bmatrix}AA^\top + BB^\top & A^\top \Delta_1 A + B^\top \Delta_2 …
- 2,712
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Estimates of product of eigenvalues gaps for Wigner matrices
Let $W_n$ be an $n\times n$ Wigner matrix$^{1}$, and let $\lambda_1\le \lambda_2\le \cdots \le \lambda_n$ be the eigenvalues of $\frac{W_n}{\sqrt{n}}$.
My question. For any fixed $i\in\{1,\dots,n\}$, …
- 2,712
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Bounds on discrepancy metric of product measures
Consider two measurable spaces $X_1 = (\mathbb{R}^m,\mathcal{B}(\mathbb{R}^m),\mu_1)$ and $X_2 = (\mathbb{R}^m,\mathcal{B}(\mathbb{R}^m),\mu_2)$ and the product spaces
$$X_1^{q} = (\times_{i=1}^q\math …
- 2,712