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arXiv · 2407.16967

Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations

Sasha Bell·Tasmin Chu·Owen Rodgers
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Abstract

We consider the least-deletion map on the Cantor space, namely the map that changes the first 1 in a binary sequence to 0, and construct product measures on $2^\mathbb{N}$ so that the corresponding Radon-Nikodym cocycles oscillate or converge to zero nonsummably along the forward geodesic of the map. These examples answer two questions of Tserunyan and Tucker-Drob. We analyze the oscillating example in terms of random walks on $\mathbb{Z}$, using the Chung-Fuchs theorem.

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Sasha Bell, Tasmin Chu, Owen Rodgers. 2024-07-24. Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations. https://arxiv.org/abs/2407.16967

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