1 citations · 1 across the 6 of their papers we have counts for
7 papers
Stability of extremal hyperplane projections of balls in
Jacek Jakimiuk
We prove stability estimates for the volume of central hyperplane projections of unit balls in , establishing the dual counterpart of the result of Chasapis,…
Geometry of the Atomic Condition
Jacek Jakimiuk, Sławomir Kolasiński, Maciej Leśniak
The class AC of integrands satisfying the atomic condition was introduced by De Philippis, De Rosa, and Ghiraldin in 2018. These integrands give rise to Almgren elliptic geometric…
Lower bounds on non-central sections of isotropic convex bodies
Jacek Jakimiuk, Daniel Murawski, Piotr Nayar
For fixed we give asymptotically sharp lower bounds on the quantity , where is a hyperplane at distance from th…
Khinchin inequalities for uniforms on spheres with a deficit
Jacek Jakimiuk, Colin Tang, Tomasz Tkocz
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
Stability of Khintchine inequalities with optimal constants between the second and the -th moment for
Jacek Jakimiuk
We give a strengthening of the classical Khintchine inequality between the second and the -th moment for with optimal constant by adding a deficit depending on the vec…
Maximal sections of the unit ball of for
Jacek Jakimiuk, Hermann König
Eskenazis, Nayar and Tkocz have shown recently some resilience of Ball's celebrated cube slicing theorem, namely its analogue in for large . We show that the complex ana…
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…