Higher order concentration for functions of weakly dependent random variables

Abstract

We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a difference operator that arises from Gibbs sampler type dynamics. Examples of such random variables include the Ising model on a graph with n nodes with general, but weak interactions, i.e. in the Dobrushin uniqueness regime, for which we prove concentration results of homogeneous polynomials, as well as random permutations, and slices of the hypercube with dynamics given by either the Bernoulli-Laplace or the symmetric simple exclusion processes.

Added concentration results for some polynomials in Ising models with external fields; streamlined a few proofs

References in corpus (5)

• Estimates of moments and tails of Gaussian chaoses
• Applications of Stein's method for concentration inequalities
• Moment inequalities for U-statistics
• Higher Order Concentration of Measure
• Concentration of Multilinear Functions of the Ising Model with Applications to Network Data

Cited by in corpus (12)

• Concentration inequalities for polynomials in $\alpha$-sub-exponential random variables
• Fluctuation results for general block spin Ising models
• Logarithmic Sobolev inequalities for finite spin systems and applications
• Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
• A note on concentration for polynomials in the Ising model
• Modified log-Sobolev inequalities and two-level concentration
• Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
• Outlier-Robust Learning of Ising Models Under Dobrushin's Condition
• Concentration inequalities on the multislice and for sampling without replacement
• Large deviations and a phase transition in the Block Spin Potts models
• Learning Restricted Boltzmann Machines with Sparse Latent Variables
• De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry