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math.PR2025
Weak dependence and optimal quantitative self-normalized central limit theorems
Moritz Jirak
Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry-Esse…
math.PR2018
Perturbation bounds for eigenspaces under a relative gap condition
Moritz Jirak, Martin Wahl
A basic problem in operator theory is to estimate how a small perturbation effects the eigenspaces of a self-adjoint compact operator. In this paper, we prove upper bounds for the…
math.PR2017
Rate of convergence for Hilbert space valued processes
Moritz Jirak
Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying…