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math.DS2026
Quantitative Convergence for Sparse Ergodic Averages in
Ben Krause, Yu-Chen Sun
We provide a unified framework to proving pointwise convergence of sparse sequences, deterministic and random, at the endpoint. Specifically, suppose that \[ a_n \in \{ \l…
math.DS2025
A Hard-Analytic Proof of "Most" Polynomial Wiener-Wintner Theorems for Infinite Measure Spaces
Ben Krause
We provide a new proof of ``most" cases of the polynomial Wiener-Wintner theorem for -finite spaces, using hard-analytic methods. Specifically, we prove that whenever $(X,μ,T)…
math.DS2025
A Unified Approach to Two Pointwise Ergodic Theorems: Double Recurrence and Return Times
Ben Krause
We present a unified approach to extensions of Bourgain's Double Recurrence Theorem and Bourgain's Return Times Theorem to integer parts of the Kronecker sequence, emphasizing stop…