Higher order concentration for functions of weakly dependent random variables
By Friedrich Götze, H. Sambale, A. Sinulis. Electronic Journal of Probability, 2018
60 citations recorded by the source corpus.
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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/124034dee94b21a443c6b76c280ff27d948161f1
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Uniform Hanson-Wright type concentration inequalities for unbounded entries via the entropy method (2018, methodology): “We consider the Ising model under Dobrushin’s condition that caught some attention recently (see Adamczak et al. (2018a) and Götze et al. (2018)).”