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8
votes
4answers
413 views

More than $n$ approximately orthonormal vectors in $R^n$

This question was asked at math.stackexchange, where it got several upvotes but no answers. It is impossible to find $n+1$ mutually orthonormal vectors in $R^n$. However, it is well established ...
3
votes
0answers
79 views

Concentration of weighted random chirp

I'm interested in seeing whether the following is true. Assume $u$ is uniform on $[0,1]$. For a fixed $x\in\mathbb{C}^n$ with $\|x\|_{2}=1$ we have \begin{align*} ...
0
votes
2answers
238 views

Weak convergence of the image of a weakly $L^1$ converging sequence

This is a follow-up on another question. Can something be said about the image of a weakly converging sequence in $L^1$? More precisely $u_k\ge 0$ $\|u_k\|_{L^1}=\int u_k=1$ $u_k$ converges to $u$ ...
2
votes
1answer
114 views

Concentration inequalities in $\ell_{\infty}$ for sums of iid random (“nice”) functions?

I'm looking for "tail-bound-like" inequalities that look like this (I state a specific setting but more general settings are interesting): Let $D$ be a distribution on a set of "nice" functions ...
0
votes
0answers
63 views

Bounding Random Quadratic Gauss sums

I'm interested in seeing whether the following is true. Assume $u$ is uniform on $[0,1]$ and $|\epsilon_k|=1$ for all $k=1,2,\ldots,n$. We have \begin{align*} ...