Uniform scaling limits for ergodic measures
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We provide an elementary proof that ergodic measures on one-sided shift spaces are ‘uniformly scaling’ in the following sense: at almost every point the scenery distributions weakly converge to a common distribution on the space of measures. Moreover, we show how the limiting distribution can be expressed in terms of, and derived from, a 'reverse Jacobian’ function associated with the corresponding measure on the space of left infinite sequences. Finally we specialise to the setting of Gibbs measures, discuss some statistical properties, and prove a Central Limit Theorem for ergodic Markov measures.
Fraser , J M & Pollicott , M 2017 , ' Uniform scaling limits for ergodic measures ' , Journal of Fractal Geometry , vol. 4 , no. 1 , pp. 1-19 . https://doi.org/10.4171/JFG/42
Journal of Fractal Geometry
© 2017, European Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.ems-ph.org / https://doi.org/10.4171/JFG/42
DescriptionJ. M. Fraser and M. Pollicott were financially supported in part by the EPSRC grant EP/J013560/1.
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