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math.DS2026
Pointwise Convergence of Random Ergodic Averages at the \(L^1\) Endpoint
Will Burstein, Lorenzo Catani, Ben Krause
In his highly influential paper, \emph{On the maximal ergodic theorem for certain subsets of the integers}, Bourgain introduced the study of pointwise convergence of ergodic averag…
math.DS2026
Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets
Félix Brokering Pinilla, Alex Iosevich, Ben Krause
Let , \[ D \subsetneq \{ 0,1,\dots,d-1\}, \qquad |D| \geq 2, \ 0 \in D \] be a finite alphabet, and define the integer Cantor set \begin{align} \mathcal{C} := \mathcal{C}…
math.DS2026
The Wiener Wintner Theorem Along the Primes
Jan Fornal, Anastasios Fragkos, Ben Krause +3
We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability sp…