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罢颈迟濒别:听Fractal uncertainty principle for discrete Cantor sets for random alphabets.

Abstract: The fractal uncertainty principle (FUP) introduced by Dyatlov-Zahl鈥�16 has seen some powerful applications in the last few years and become a hot topic in harmonic analysis. In this talk, we study the FUP for discrete Cantor sets from a probabilistic perspective. We show that randomizing our alphabets gives a quantifiable improvement over the current 鈥渮ero鈥� and 鈥減ressure鈥� bounds. In turn, this provides the best possible exponent when the Cantor sets enjoy either the strongest Fourier decay or additive energy assumptions. This is joint work with Xiaolong Han (Cal. State Northridge).

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