We prove new quantitative additive energy estimates for a large class of
porous measures which include, for example, all Hausdorff measures of
Ahlfors-David subsets of the real line of dimension strictly between 0
and 1. We are able to obtain improved quantitative results over existing
additive energy bounds for Ahlfors-David sets by avoiding the use of
inverse theorems in additive combinatorics and instead opting for a more
direct approach which involves the use of concentration of measure
inequalities. We discuss some connections with Bourgain's sum-product
theorem.
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