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Local dimensions, Bernoulli convolutions and self-affine measures

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If you have a question about this talk, please contact Yonatan Gutman.

In this talk I’ll look at local dimensions for certain self affine and self similar measures. Local dimensions look at the local scaling property of a measure and may take very different values for different points. I’ll start by describing one well known situation where this is the case, that is for self-simialr measures satisfying the open set condition. I’ll then turn attention to two variants of this case, one will be Bernoulli convolutions and the other will be certain self-affine measures which project to Bernoulli convolutions. All new results described are joint with Pablo Shmerkin and Boris Solomyak.

This talk is part of the Discrete Analysis Seminar series.

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