Sean Skinner

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math.DS2026

Primitive Averages, Directional Expansivity, and Quantitative Twisted Recurrence for Ergodic $Z^{d}$ -Actions

Rickard Cullman, Sean Skinner

We prove two new results about probability preserving actions $T : Z^{d} ↷ (X, I^¼)$ . First, for a function $f \in L^{2} (I^¼)$ , we provide an explicit formula for the…

math.DS2024

Quantitative expansivity for ergodic $Z^{d}$ actions

Alexander Fish, Sean Skinner

We study expansiveness properties of positive measure subsets of ergodic $Z^{d}$ -actions along two different types of structured subsets of $Z^{d}$ , namely, cyclic su…

math.DS2024

An inverse of Furstenberg's correspondence principle and applications to nice recurrence

Alexander Fish, Sean Skinner

We prove an inverse of Furstenberg's correspondence principle stating that for all measure preserving systems $(X, I^¼, T)$ and $A \subset X$ measurable there exists a set $E \subset \…

Primitive Averages, Directional Expansivity, and Quantitative Twisted Recurrence for Ergodic Zd-Actions

Quantitative expansivity for ergodic Zd actions

An inverse of Furstenberg's correspondence principle and applications to nice recurrence

Primitive Averages, Directional Expansivity, and Quantitative Twisted Recurrence for Ergodic $Z^{d}$ -Actions

Quantitative expansivity for ergodic $Z^{d}$ actions