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Results tagged with pr.probability
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user 120302
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
2
answers
2k
views
The norm of isotropic sub-Gaussian random vector may not be sub-Gaussian
Suppose $X$ is a isotropic sub-Gaussian $n$-dimensional random vector (i.e. $EXX^T=I_n$, and for any unit vector $u$,$\|\left<X,u\right>\|_{\psi_2}\le K$). It is said that $\|X\|_2-\sqrt n$ may not be …
- 601
7
votes
3
answers
2k
views
Prove that a sub-Gaussian random vector over a finite set $S \subset\mathbb R^n$ implies tha...
Let $X$ be an isotropic random vector (i.e. $E[XX^T]=I_n$) and $X$ takes value in a finite set $S \subset\mathbb R^n$. If $X$ is a sub-Gaussian random vector and the norm $\|X\|_{\psi_2}\le C$ where $ …
- 601
10
votes
1
answer
10k
views
Expectation of the norm of a random vector
Suppose $X$ is a random vector denoted as $(X_1,\cdots,X_n)$, where $X_1,\cdots,X_n$ are iid random variables with sub-Gaussian distributions. For all $i$, suppose $E[X_i^2]=1$ for simplicity and $\|X …
- 601