Higher order concentration for functions of weakly dependent random variables
Götze, Friedrich
Götze
Friedrich
Sambale, Holger
Sambale
Holger
Sinulis, Arthur
Sinulis
Arthur
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 Glauber type dynamics. Examples include the Ising model on a graph with n sites 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.
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Univ Washington, Dept Mathematics
2019