Large deviations, moderate deviations, and the KLS conjecture

DOI10.1016/j.jfa.2020.108779zbMath1486.60049arXiv2003.11442OpenAlexW3089521725MaRDI QIDQ2210452

David Alonso-Gutiérrez, Joscha Prochno, Christoph Thäle

Publication date: 6 November 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.11442

zbMATH Keywords

large deviation principleasymptotic geometric analysis\(\ell_p^n\)-ballsKannan-Lovasz-Simonovits (KLS) conjecture

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Large deviations (60F10) Probabilistic methods in Banach space theory (46B09) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Asymptotic theory of convex bodies (52A23)

Related Items (5)

Projections of the uniform distribution on the cube: a large deviation perspective ⋮ Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures ⋮ An asymptotic thin shell condition and large deviations for random multidimensional projections ⋮ Thin-shell theory for rotationally invariant random simplices ⋮ Limit theorems for random points in a simplex

Cites Work

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• Poincaré inequalities and moment maps
• A central limit theorem for projections of the cube
• Large deviations for weighted sums of stretched exponential random variables
• Approaching the Kannan-Lovász-Simonovits and variance conjectures
• Large deviations for random projections of \(\ell^{p}\) balls
• An isoperimetric inequality on the \(\ell _p\) balls
• Large deviations techniques and applications.
• A geometric inequality and the complexity of computing volume
• Computing the volume is difficult
• Large deviations for high-dimensional random projections of \(\ell_p^n\)-balls
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Isoperimetric problems for convex bodies and a localization lemma
• Sanov-type large deviations in Schatten classes
• Remarks on non-interacting conservative spin systems: the case of gamma distributions
• Gaussian fluctuations for high-dimensional random projections of \(\ell_p^n\)-balls
• A central limit theorem for convex sets
• SPECTRAL GAP FOR SOME INVARIANT LOG‐CONCAVE PROBABILITY MEASURES
• On the infimum convolution inequality
• A random polynomial-time algorithm for approximating the volume of convex bodies
• A Simple Analytic Proof of an Inequality by P. Buser
• Some connections between isoperimetric and Sobolev-type inequalities
• A conditional limit theorem for high-dimensional ℓᵖ-spheres
• Limit theorems for random simplices in high dimensions
• High-dimensional limit theorems for random vectors in ℓpn-balls
• On Isoperimetric Constants for Log-Concave Probability Distributions
• Large deviations
• CLT and the volume of intersections of \(\ell_p^n\)-balls

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