Paata Ivanisvili

activity

20232025

most citedOn sharp isoperimetric inequalities on the hypercube

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.FA2025

Multiversion of the Hausdorff--Young inequality

Paata Ivanisvili, Pavlos Kalantzopoulos

We consider a family of jointly Gaussian random vectors $ξ_{j} \in R^{k_{j}}$ , each standard normal but possibly correlated, and investigate when\[ \mathbb{E}\, F\!\Bigl(B\big…

math.FA2024

$(P, Q)$ complex hypercontractivity

Paata Ivanisvili, Pavlos Kalantzopoulos

Let $ξ$ be the standard normal random vector in $R^{k}$ . Under some mild growth and smoothness assumptions on any increasing $P, Q : [0, \infty) \mapsto [0, \infty)$ we sh…

math.PR2024

Sharpening the gap between $L^{1}$ and $L^{2}$ norms

Paata Ivanisvili, Yonathan Stone

We refine the classical Cauchy--Schwartz inequality $∥ X ∥_{1} \leq ∥ X ∥_{2}$ by demonstrating that for any $p$ and $q$ with $q > p > 2$ , there exists a constant $C = C (p, q)$ such that…

math.CO2024

Discrete Brunn-Minkowski Inequality for subsets of the cube

Lars Becker, Paata Ivanisvili, Dmitry Krachun +1

We show that for all $A, B \subseteq {0, 1, 2}^{d}$ we have $∣ A + B ∣ \geq (∣ A ∣∣ B ∣)^{l o g (5) / (2 l o g (3))} .$ We also show that for all finite $A, B \subset Z^{d}$ , and any $V…

math.CA2023★ 1 cited

On sharp isoperimetric inequalities on the hypercube

David Beltran, Paata Ivanisvili, José Madrid

We prove the sharp isoperimetric inequality $E h_{A}^{l o g_{2} (3/2)} \geq μ (A)^{*} (lo g_{2} (1/ μ (A)^{*}))^{l o g_{2} (3/2)}$ for all sets $A \subseteq {0, 1}^{n}$ , wher…