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BGU Probability and Ergodic Theory (PET) seminar

Equidistribution of Discrepancy Sequences (Joint with Dolgopyat)

May 16, 11:10—12:00, 2024, -101


Omri Sarig (Weizmann Institute of Science)


Let \alpha be an irrational number and let J be a sub interval of [0,1]. The discrepancy sequence of J is D(N), where

D(N):=the number of visits of n\alpha mod 1 to J for 1<n<N minus N J .

Weyl’s Equidistribution Theorem says that D(N)=o(N). But this sequence is not necessarily bounded.

I will characterize the irrationals \alpha of bounded type, for which the discrepancy sequence of the interval [0,1/2] is equidistributed on (1/2)Z . This is joint work with Dima Dolgopyat.

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