Pointwise convergence of multiple ergodic averages for mixing transformations

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Kuca (2026), Joint ergodicity - 40 years on (survey) evidence for this event

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Pointwise convergence of multiple ergodic averages for mixing transformations parent of this event

Pointwise convergence of multiple ergodic averages for mixing transformations evidence for this event

Claims Theorem 1.1: for every invertible mixing probability-preserving $T$ (no standardness, no mixing rate), every $n\ge2$ and bounded $f_1,\dots,f_n$, $\frac1N\sum_{k\le N}\prod_j f_j(T^{jk}x)\to\prod_j\int f_j$ almost everywhere along all $N$. Companions treat $n=3,4$ and three distinct nonzero slopes of either sign for mixing $T$. Lemma 2.5 of the principal manuscript also states almost-everywhere convergence of averages of at most three functions at distinct positive slopes on every standard system, derived from the companion's oscillation estimate. It does NOT settle the general question for $n\ge4$ on non-mixing systems, nor polynomial iterates. parent of this event

Companion: Pointwise convergence of fourfold ergodic averages for mixing transformations evidence for this event

Companion: Triple ergodic averages with distinct integer slopes evidence for this event

VibeMathed record: Pointwise convergence of multiple ergodic averages for mixing transformations evidence for this event

Companion: Pointwise convergence of triple ergodic averages for mixing transformations evidence for this event