Peter van Hintum

activity

20202025

most citedInversion of Bayesian Networks

1 citations · 3 across the 11 of their papers we have counts for

collaborators

11 papers

math.FA2025

Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities

Alessio Figalli, Peter van Hintum, Marius Tiba

The Borell-Brascamp-Lieb inequality is a classical extension of the Prékopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The st…

math.AP2024

Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality, applicable to bounded measurable sets $A$ and $B$ in $R^{d}$ , states that $∣ A + B ∣^{1/ d} \geq ∣ A ∣^{1/ d} + ∣ B ∣^{1/ d}$ . Equality is achieved if and…

math.AP2023

Sharp quantitative stability of the Brunn-Minkowski inequality

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $R^{n}$ , we have $∣ A + B ∣^{1/ n} \geq ∣ A ∣^{1/ n} + ∣ B ∣^{1/ n}$ . Also, equality holds if and on…

math.CO2023

Sharp bounds for the Tao-Vu Discrete John's Theorem

Peter van Hintum, Peter Keevash

Tao and Vu showed that every centrally symmetric convex progression $C \subset Z^{d}$ is contained in a generalised arithmetic progression of size $d^{O (d^{2})} # C$ . Berg and…

math.CO2023★ 1 cited

On Ruzsa's discrete Brunn-Minkowski conjecture

Peter van Hintum, Peter Keevash, Marius Tiba

We prove a conjecture by Ruzsa from 2006 on a discrete version of the Brunn-Minkowski inequality, stating that for any $A, B \subset Z^{k}$ and $ε > 0$ with $B$ not contained in…

math.MG2023

The sharp doubling threshold for approximate convexity

Peter van Hintum, Peter Keevash

We show for $A, B \subset R^{d}$ of equal volume and $t \in (0, 1/2]$ that if $∣ t A + (1 - t) B ∣ < (1 + t^{d}) ∣ A ∣$ , then (up to translation) $∣ co (A \cup B) ∣/∣ A ∣$ is bounded. This esta…

math.CO2023

Locality in Sumsets

Peter van Hintum, Peter Keevash

Motivated by the Polynomial Freiman-Ruzsa (PFR) Conjecture, we develop a theory of locality in sumsets, with applications to John-type approximation and sets with small doubling. F…

cs.LG2022★ 1 cited

Inversion of Bayesian Networks

Jesse van Oostrum, Peter van Hintum, Nihat Ay

Variational autoencoders and Helmholtz machines use a recognition network (encoder) to approximate the posterior distribution of a generative model (decoder). In this paper we stud…

math.MG2022

Towards Hadwiger's conjecture via Bourgain Slicing

Marcelo Campos, Peter van Hintum, Robert Morris +1

In 1957, Hadwiger conjectured that every convex body in $R^{d}$ can be covered by $2^{d}$ translates of its interior. For over 60 years, the best known bound was of the form $…

math.FA2020★ 1 cited

Sharp L1 Inequalities for Sup-Convolution

Peter van Hintum, Hunter Spink, Marius Tiba

Given a compact convex domain $C \subset R^{k}$ and bounded measurable functions $f_{1}, \dots, f_{n} : C \to R$ , define the sup-convolution $(f_{1} * \dots * f_{n}) (z)$ t…

math.NT2020

Sets in $Z^{k}$ with doubling $2^{k} + δ$ are near convex progressions

Peter van Hintum, Hunter Spink, Marius Tiba

For $δ > 0$ sufficiently small and $A \subset Z^{k}$ with $∣ A + A ∣ \leq (2^{k} + δ) ∣ A ∣$ , we show either $A$ is covered by $m_{k} (δ)$ parallel hyperplanes, or satisfies $|\widehat{\operat…

Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities

Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation

Sharp quantitative stability of the Brunn-Minkowski inequality

Sharp bounds for the Tao-Vu Discrete John's Theorem

On Ruzsa's discrete Brunn-Minkowski conjecture

The sharp doubling threshold for approximate convexity

Locality in Sumsets

Inversion of Bayesian Networks

Towards Hadwiger's conjecture via Bourgain Slicing

Sharp L1 Inequalities for Sup-Convolution

Sets in Zk with doubling 2k+δ are near convex progressions

Sets in $Z^{k}$ with doubling $2^{k} + δ$ are near convex progressions