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arXiv · 1502.05610

Uniform scaling limits for ergodic measures

Jonathan M. Fraser·Mark Pollicott
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Abstract

We prove that ergodic measures on one-sided shift spaces are uniformly scaling in the sense of Gavish. That is, given a shift ergodic measure we prove that at almost every point the scenery distributions weakly converge to a common distribution on the space of measures. Moreover, we give an explicit description of the limiting distribution in terms of a `reverse Jacobian' function associated with the corresponding measure on the space of left infinite sequences.

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Jonathan M. Fraser, Mark Pollicott. 2015-02-19. Uniform scaling limits for ergodic measures. https://arxiv.org/abs/1502.05610

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