Decomposition of Random Walk Measures on the One-Dimensional Torus

Tom Gilat

Research output: Contribution to journalArticlepeer-review


The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a "sufficiently large" subset S of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one μ1 has the property that the random walk with initial distribution μ1 evolved by the action of S equidistributes very fast. The second measure μ2 in the decomposition is concentrated on very small neighborhoods of a small number of points.

Original languageEnglish
Article number3
JournalDiscrete Analysis
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020. Tom Gilat


The work presented in this paper comprises most of my PhD dissertation written at the Hebrew University. I wish to thank my advisor, Prof. Elon Lindenstrauss, for having me as a student, acquainting me with the techniques and ideas which consist of this work, guiding me and more. I am deeply grateful for that. I would also like to thank Prof. Barak Weiss and Prof. Tamar Ziegler, who served on my PhD committee, for following the process of the work and asking important questions. I would like to thank Prof. Mike Hochman for his remarks and help. In addition, I wish to thank the Hebrew University and the Einstein Institute for being such a pleasant home. Lastly, I wish to thank the anonymous referees who meticulously read my thesis. One of the referees summarized the work so well that I could not avoid using his descriptions in the introduction of this paper.

FundersFunder number
Hebrew University of Jerusalem


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