A. I. Bufetov, B. Solomyak, “Limit theorems for self-similar tilings”, Communications in Mathematical Physics, 2013, Volume 319, Issue 3, Pages 761

Loading [MathJax]/jax/output/SVG/config.js

Communications in Mathematical Physics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	Main page
	About this project
	Software
	Classifications
	Links
	Terms of Use

	Search papers
	Search references

	RSS
	Current issues
	Archive issues
	What is RSS

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Communications in Mathematical Physics, 2013, Volume 319, Issue 3, Pages 761–769
DOI: https://doi.org/10.1007/s00220-012-1624-7 (Mi cmph6)

This article is cited in 19 scientific papers (total in 19 papers)

Limit theorems for self-similar tilings

A. I. Bufetov^abcde, B. Solomyak^f

^a Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia
^b Natl Res Univ, Higher Sch Econ, Moscow, Russia
^c Rice Univ, Dept Math, Houston, TX 77005
^d VA Steklov Math Inst, Moscow 117333, Russia
^e Aix Marseille Univ, Lab Anal, CNRS, Marseille, France
^f Univ Washington, Dept Math, Seattle, WA 98195 USA

Citations (19)

DOI: https://doi.org/10.1007/s00220-012-1624-7

Abstract: We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.

Funding agency	Grant number
Dynasty Foundation
Alfred P. Sloan Foundation
Simons Foundation
Ministry of Education and Science of the Russian Federation	MK 6734.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research	10-01-93115 11-01-00654
National Science Foundation	DMS-0968879
A. B. is an Alfred P. Sloan Fellow, a Dynasty Foundation Fellow, and an IUM-Simons Fellow. He is supported in part by the Grant MK 6734.2012.1 of the President of the Russian Federation, by the Programme on Dynamical Systems and Mathematical Control Theory of the Presidium of the Russian Academy of Sciences, by RFBR-CNRS grant 10-01-93115 and by the RFBR grant 11-01-00654. B. S. is supported in part by NSF grant DMS-0968879.

Received: 03.02.2012
Accepted: 26.03.2012

Bibliographic databases:

Document Type: Article

Language: English

Linking options:

https://www.mathnet.ru/eng/cmph6

This publication is cited in the following 19 articles:

A. Bufetov, B. Solomyak, “Self-similarity and spectral theory: on the spectrum of substitutions”, St. Petersburg Math. J., 34:3 (2023), 313
BORIS SOLOMYAK, RODRIGO TREVIÑO, “Spectral cocycle for substitution tilings”, Ergod. Th. Dynam. Sys., 2023, 1
Minsung Kim, “Limit theorems for higher rank actions on Heisenberg nilmanifolds”, DCDS, 42:9 (2022), 4347
Rodrigo Treviño, Agnieszka Zelerowicz, “Statistical Properties of Lorentz Gases on Aperiodic Tilings, Part 1”, Commun. Math. Phys., 396:3 (2022), 1305
Scott Schmieding, Rodrigo Treviño, “Random substitution tilings and deviation phenomena”, DCDS, 41:8 (2021), 3869
José Aliste-Prieto, Betseygail Rand, Lorenzo Sadun, “Rotation Numbers and Rotation Classes on One-Dimensional Tiling Spaces”, Ann. Henri Poincaré, 22:7 (2021), 2161
Alexander I. Bufetov, Boris Solomyak, “Hölder regularity for the spectrum of translation flows”, J. Éc. Polytech., Math., 8 (2021), 279–310
Rodrigo Treviño, “Tilings and traces”, Journal of Mathematical Physics, 62:7 (2021)
Dmitry Dolgopyat, Bassam Fayad, “Deviations of ergodic sums for toral translations II. Boxes”, Publ.math.IHES, 132:1 (2020), 293
Nicolas Bédaride, Arnaud Hilion, Martin Lustig, “Graph towers, laminations and their invariant measures”, J. London Math. Soc., 101:3 (2020), 1112
Valérie Berthé, Paulina Cecchi Bernales, “Balancedness and coboundaries in symbolic systems”, Theoretical Computer Science, 777 (2019), 93
ARTEMI BERLINKOV, BORIS SOLOMYAK, “Singular substitutions of constant length”, Ergod. Th. Dynam. Sys., 39:9 (2019), 2384
ALAN HAYNES, ANTOINE JULIEN, HENNA KOIVUSALO, JAMES WALTON, “Statistics of patterns in typical cut and project sets”, Ergod. Th. Dynam. Sys., 39:12 (2019), 3365
Michael Bromberg, Corinna Ulcigrai, “A temporal central limit theorem for real-valued cocycles over rotations”, Ann. Inst. H. Poincaré Probab. Statist., 54:4 (2018)
Scott Schmieding, Rodrigo Treviño, “Self Affine Delone Sets and Deviation Phenomena”, Commun. Math. Phys., 357:3 (2018), 1071
Carl P. Dettmann, Jens Marklof, Andreas Strömbergsson, “Universal Hitting Time Statistics for Integrable Flows”, J Stat Phys, 166:3-4 (2017), 714
Francesco Cellarosi, Jens Marklof, “Quadratic Weyl sums, automorphic functions and invariance principles”, Proc. London Math. Soc., 113:6 (2016), 775
A. I. Bufetov, B. Solomyak, “On the modulus of continuity for spectral measures in substitution dynamics”, Adv. Math., 260 (2014), 84–129
Jory Griffin, Jens Marklof, “Limit theorems for skew translations”, Journal of Modern Dynamics, 8:2 (2014), 177

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	191

Что такое QR-код?

Registration to the website

Logotypes