Daniel Murawski

activity

20222026

most citedLog-concavity and discrete degrees of freedom

1 citations · 1 across the 3 of their papers we have counts for

collaborators

4 papers

math.MG2026

Lower bounds on non-central sections of isotropic convex bodies

Jacek Jakimiuk, Daniel Murawski, Piotr Nayar

For fixed $t_{0} \in [0, 3]$ we give asymptotically sharp lower bounds on the quantity $L_{K} vol_{d - 1} (K \cap H)$ , where $H$ is a hyperplane at distance $t_{0} L_{K}$ from th…

math.PR2025

On the optimal $L_{p}$ - $L_{4}$ Khintchine inequality

Adam Barański, Daniel Murawski, Piotr Nayar +1

We derive optimal dimension independent constants in the classical Khintchine inequality between the $p$ th and fourth moment for $p \geq 4$ . As an application we deduce stability est…

math.PR2022

Comparing moments of real log-concave random variables

Daniel Murawski

We show that for every mean zero log-concave real random variable $X$ one has $∥ X ∥_{p} \leq \frac{p}{q} ∥ X ∥_{q}$ for $p \geq q \geq 1$ , going beyond the well-known case of symmetri…

math.PR2022★ 1 cited

Log-concavity and discrete degrees of freedom

Jacek Jakimiuk, Daniel Murawski, Piotr Nayar +1

We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove that geometric distribution minimises Rényi entropy of order infinity under fixed…

Lower bounds on non-central sections of isotropic convex bodies

On the optimal Lp​-L4​ Khintchine inequality

Comparing moments of real log-concave random variables

Log-concavity and discrete degrees of freedom

On the optimal $L_{p}$ - $L_{4}$ Khintchine inequality