Higher order concentration in presence of Poincaré-type inequalities

2018/03/14 by Friedrich Götze, Götze, Friedrich, Holger Sambale +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Point processes and geometric inequalities #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1803.05190

Abstract

We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d-1 for any d ∈ ℕ. Here we focus on differentiable functions on the Euclidean space in presence of a Poincaré-type inequality. The bounds are based on d-th order derivatives.

Cited by

• Some notes on higher order concentration of measure
• Conditional central limit theorems for exponential random graphs

Related

• Some notes on higher order concentration of measure
• Second Order Concentration via Logarithmic Sobolev Inequalities
• Concentration of measure via approximated Brunn--Minkowski inequalities
• Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order
• Matrix Poincaré inequalities and concentration