Dimension of Self-similar Measures and Additive Combinatorics
51 mins 12 secs,
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About this item
| Description: |
Hochman, M (Hebrew University of Jerusalem)
Wednesday 02 July 2014, 10:00-10:50 |
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| Created: | 2014-07-11 18:30 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Hochman, M |
| Language: | eng (English) |
| Abstract: | I will discuss recent progress on the problem of computing the dimension of a self-similar set or measure in R in the presence of non-trivial overlaps. It is thought that unless the overlaps are "exact" (an essentially algebraic condition), the dimension achieves the trivial upper bound. I will present a weakened version of this that confirms the conjecture in some special cases. A key ingredient is a theorem in additive combinatorics that describes in a statistical sense the structure of measures whose convolution has roughly the same entropy at small scales as the original measure. As time permits, I will also discuss the situation in Rd. |
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