Roman Vershynin

collaborators

3 papers

math.CO2025

Covering the hypercube, the uncertainty principle, and an interpolation formula

Paata Ivanisvili, Ohad Klein, Roman Vershynin

We show that the minimal number of skewed hyperplanes that cover the hypercube ${0, 1}^{n}$ is at least $\frac{n}{2} + 1$ , and there are infinitely many $n$ 's when the hypercube can…

math.CO2024

Hamiltonicity of Sparse Pseudorandom Graphs

Asaf Ferber, Jie Han, Dingjia Mao +1

We show that every $(n, d, I^»)$ -graph contains a Hamilton cycle for sufficiently large $n$ , assuming that $d \geq lo g^{6} n$ and $I^» \leq c d$ , where $c = \frac{1}{70000}$ . This significa…

math.FA2024

Jackson's inequality on the hypercube

Paata Ivanisvili, Roman Vershynin, Xinyuan Xie

We investigate the best constant $J (n, d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on…