Author

E. Ercan

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Preprint Oct 2026

Lorentzian entropy, subgaussian matrix concentration, and sharp functional inequalities for all matroids

We prove complete entropy contraction for homogeneous Lorentzian laws and derive subgaussian matrix concentration and sharp functional inequalities for every matroid. Uniform retention of $\ell$ out of $r$ particles contracts matrix entropy by the optimal universal factor $\ell/r$, in every finite matrix dimension and...

E. Ercan · 0 citations

Preprint Sep 2026

Vector balancing in convex order

It is proved that Covariance-matched analytic uniformly log-concave sources can have a greatest useful-data-only private release with infinite information, while no greatest full-data release exists.

E. Ercan · 0 citations

Preprint Sep 2026

A $(\log n)^{1/4}$ Bound for the Koml\'os Problem

Let $A\in\mathbb{R}^{m\times n}$ have columns of Euclidean norm at most one. We prove that $\operatorname{disc}(A)\le2395\left(1+\log_+\frac n9\right)^{1/4}+2\sqrt2$. Here $\log_+t=\max\{0,\log t\}$. Building on Bansal and Jiang's affine spectral independence framework, we remove the $(\log\log n)^{7/4}$ factor from th...

E. Ercan · 3 citations