On the failure of concentration for the \(\ell_\infty\)-ball

DOI10.1007/s11856-015-1265-6zbMath1339.28004arXiv1309.3315OpenAlexW2301564384MaRDI QIDQ273089

Tim D. Austin

Publication date: 21 April 2016

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3315

zbMATH Keywords

compact metric space \(X\)probability measure on \(X\)support of measure

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Measures and integrals in product spaces (28A35)

Related Items (3)

Quantum Talagrand, KKL and Friedgut's theorems and the learnability of quantum Boolean functions ⋮ Unnamed Item ⋮ Juntas in theℓ₁-grid and Lipschitz maps between discrete tori

Cites Work

• Unnamed Item
• Geometric influences
• A structure theorem for Boolean functions with small total influences
• Logarithmic Sobolev inequalities and hypercontractive estimates on the circle
• Boolean functions with low average sensitivity depend on few coordinates
• On Russo's approximate zero-one law
• The influence of variables in product spaces
• Infinite dimensional isoperimetric inequalities in product spaces with the supremum distance
• Independent sets in graph powers are almost contained in juntas
• Bi-Lipschitz bijection between the Boolean cube and the Hamming ball
• Decision Trees and Influences of Variables Over Product Probability Spaces
• Logarithmic Sobolev Inequalities
• Every monotone graph property has a sharp threshold
• Influences in Product Spaces: KKL and BKKKL Revisited
• Hypercontractive Measures, Talagrand’s Inequality, and Influences
• Analysis and Geometry of Markov Diffusion Operators
• The geometry of Markov diffusion generators

This page was built for publication: On the failure of concentration for the \(\ell_\infty\)-ball