9 problems

Let $X$ be a random vector, and for $h\in\mathbb{S}^{d-1}$ define … The main theorem proves the corresponding characterization in dimension $d=2$ using a random sample of two proje…

Let $X$ be a random vector in $\mathbb{R}^d$, and let $d$ independent random projection directions be sampled. In dimension two, agreement between the projections of a distribution…

Projected $\ell_1$-norm concentration conjecture. There is a constant $c$ such that

Let $X$ be a random vector in $\mathbb{R}^n$ with independent and identically distributed entries, … Assume that $\mathbb{E}x_1=0$, $\mathbb{E}x_1^2=1$, and…

Let $\mathcal K_{k,p}$ be the compact set encoding the possible exponentially likely deviations of the projection $\mu_{V_{k,n}}$ in the large-deviation principle for random projec…

Let $K$ be an isotropic convex body in $\mathbb{R}^n$, and consider its $k$-dimensional marginals, equivalently, orthogonal projections onto $k$-dimensional subspaces. Anttila–Ball…

The vanishing-dimension LDP conjecture. In this case, the large deviation principle for $\boldsymbol{\\|P_E X\\|}$ is the same as the large deviation principle for…

Non-Gaussian minimizer conjecture. For every $p\in(2,\infty)$ and $w\in(-1,1)\setminus\{0\}$, the minimizer in is not $\mu_2$. Similarly, for every $\gamma\in\mathcal{T}_p$ and…

Common-phenomenon conjecture. The observation that rare events can be discarded without harming the utilities under consideration should be a common phenomenon rather than being sp…