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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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