The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.
Optimum bounds for the distributions of martingales in banach spaces.The Annals of Probability, pages 1679–1706
3 Pith papers cite this work. Polarity classification is still indexing.
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Derives |κ_n(X)| ≤ C_n M_n(X) with C_n ~ (n-1)! / ρ^n (ρ ≥ ln 2) via moment-cumulant partitions and product inequalities, improving on prior n^n-type bounds.
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.
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Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains
The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.
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Explicit Universal Bounds for Cumulants via Moments
Derives |κ_n(X)| ≤ C_n M_n(X) with C_n ~ (n-1)! / ρ^n (ρ ≥ ln 2) via moment-cumulant partitions and product inequalities, improving on prior n^n-type bounds.
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Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.