Concentration Inequalities for Non-Lipschitz Functions
summary
Shows that if a vector satisfies a Sobolev-type inequality (e.g. log-Sobolev/Gaussian) then moments and tails of C^d functions are controlled by concrete norms of derivatives: growth terms like sqrt(p)·HS norm and p·operator norm appear, obtained by iterating the inequality and inserting independent Gaussians plus decoupling and symmetrization. Results are optimal for Gaussian chaoses, extend to tetrahedral polynomials in independent sub-Gaussian Bernoulli (p) variables, and yield sharp upper-tail bounds for subgraph counts and eigenvalue statistics in certain regimes.
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