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Deviations of ergodic sums for toral tra...

Dolgopyat, Dmitry...

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Deviations of ergodic sums for toral translations II. Boxes by Dolgopyat, Dmitry ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We study the Kronecker sequence $\{n\alpha\}_{n\leq N}$ on the torus ${\mathbb T}^d$ when $\alpha$ is uniformly distributed on ${\mathbb T}^d.$ We show that the discrepancy of the number of visits of this sequence to a random box, normalized by $\ln^d N$, converges as $N\to\infty$ to a Cauchy distribution. The key ingredient of the proof is a Poisson limit theorem for the Cartan action on the space of $d+1$ dimensional lattices.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1211.4323

Citation

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AMA 11th EditionReferences

Dolgopyat, Dmitry. Deviations of ergodic sums for toral translations II. Boxes. Australian National University. August 11, 2023. Accessed October 01, 2025. https://online.provdatabase.com/cite/16041

APA 7th EditionReferences

Dolgopyat, Dmitry. (2023). Deviations of ergodic sums for toral translations II. Boxes. Australian National University. https://online.provdatabase.com/cite/16041

Chicago 17th EditionReferences

Dolgopyat, Dmitry. Deviations of ergodic sums for toral translations II. Boxes. Australian National University. 2023. https://online.provdatabase.com/cite/16041

HarvardReferences

Dolgopyat, Dmitry. (2023). Deviations of ergodic sums for toral translations II. Boxes. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/16041. (Accessed 01 October 2025).

Harvard AustraliaReferences

Dolgopyat, Dmitry, 2023, Deviations of ergodic sums for toral translations II. Boxes, Australian National University, viewed 01 October 2025, <https://online.provdatabase.com/cite/16041>

MLA 9th EditionWorks Cited

Dolgopyat, Dmitry. Deviations of ergodic sums for toral translations II. Boxes. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/16041.

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