Concentration inequalities for log-concave sequences

We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree of log-concavity. Along the way, we recover, improve, and simplify several results existing in the literature. Our approach is based on majorization in the convex order.

• Publication year

  2022

• Venue

  Unknown venue

• Publication date

  2022-05-17

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2205.08293
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Log-concavity and discrete degrees of freedom

  2022cited by this paper
• Combinatorics and Hodge theory

  2022cited by this paper
• Concentration inequalities for ultra log-concave distributions

  2021influential reference
• A discrete complement of Lyapunov's inequality and its information theoretic consequences

  2021cited by this paper
• Log-concave poset inequalities

  2021cited by this paper
• Reversal of Rényi Entropy Inequalities Under Log-Concavity

  2020cited by this paper
• Geometric and Functional Inequalities for Log-Concave Probability Sequences

  2020cited by this paper
• Concentration functions and entropy bounds for discrete log-concave distributions

  2020influential reference
• Lagrangian geometry of matroids

  2020cited by this paper
• Log-concavity of matroid h-vectors and mixed Eulerian numbers

  2020cited by this paper
• Lorentzian polynomials.

  2019cited by this paper
• Logarithmic concavity of Schur and related polynomials

  2019cited by this paper
• Simplicial generation of Chow rings of matroids

  2019cited by this paper
• Concentration of the Intrinsic Volumes of a Convex Body

  2018influential reference
• Log-Concave Polynomials III: Mason's Ultra-Log-Concavity Conjecture for Independent Sets of Matroids

  2018cited by this paper
• Correlation bounds for fields and matroids

  2018cited by this paper
• Tail bounds for sums of geometric and exponential variables

  2017influential reference
• Forward and Reverse Entropy Power Inequalities in Convex Geometry

  2016influential reference
• Unimodality, log-concavity, real-rootedness and beyond

  2015cited by this paper
• Log-Concavity and Strong Log-Concavity: a review.

  2014cited by this paper
• Concentration Inequalities: A Nonasymptotic Theory of Independence

  2013cited by this paper
• h-Vectors of matroids and logarithmic concavity

  2012cited by this paper
• Log-concavity of characteristic polynomials and the Bergman fan of matroids

  2011cited by this paper
• Concentration of the information in data with log-concave distributions

  2010cited by this paper
• Gaussian concentration for a class of spherically invariant measures

  2010influential reference
• Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs

  2010cited by this paper
• Totally Positive Matrices

  2009cited by this paper
• On the Maximum Entropy Properties of the Binomial Distribution

  2008cited by this paper
• A central limit theorem for convex sets

  2006cited by this paper
• Inequalities

  2006cited by this paper
• Spectral Gap and Concentration for Some Spherically Symmetric Probability Measures

  2003cited by this paper
• Binomial and Poisson distributions as maximum entropy distributions

  2001cited by this paper
• Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros

  1997cited by this paper
• Combinatorics and Total Positivity

  1995cited by this paper
• CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY

  1994cited by this paper
• Inequalities between intrinsic volumes

  1991cited by this paper
• Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry a

  1989cited by this paper
• Unimodal, log-concave and Pólya frequency sequences in combinatorics

  1989cited by this paper
• Uniform conditional variability ordering of probability distributions

  1985influential reference
• A Threshold for Log-Concavity for Probability Generating Functions and Associated Moment Inequalities

  1972influential reference
• Generalized convex inequalities

  1963cited by this paper

• Log-concavity and concentration bounds for a single gap between GUE eigenvalues

  2026influential citation
• From simplex slicing to sharp reverse H\"older inequalities

  2025cites this paper
• A note on the maximum probability of ultra log-concave distributions

  2025influential citation
• On Convex Functions of Gaussian Variables

  2025cites this paper
• Anti-concentration inequalities for log-concave variables on the real line

  2025cites this paper
• On the Missing Factor in Some Concentration Inequalities for Martingales

  2024influential citation
• Improved thresholds for e-values

  2024influential citation
• A note on statistical distances for discrete log-concave measures

  2023influential citation
• Entropy-variance inequalities for discrete log-concave random variables via degree of freedom

  2022cites this paper
• On a Conjecture of Feige for Discrete Log-Concave Distributions

  2022cites this paper
• Bernoulli sums and Rényi entropy inequalities

  2021cites this paper