Limit Theorems for Self-Similar Tilings

Alexander I. Bufetov; Boris Solomyak

doi:10.1007/s00220-012-1624-7

Limit Theorems for Self-Similar Tilings

Alexander I. Bufetov, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	761-789
Number of pages	29
Journal	Communications in Mathematical Physics
Volume	319
Issue number	3
DOIs	https://doi.org/10.1007/s00220-012-1624-7
State	Published - May 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-012-1624-7

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title = "Limit Theorems for Self-Similar Tilings",

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.",

author = "Bufetov, \{Alexander I.\} and Boris Solomyak",

note = "Funding Information: 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. Funding Information: B. S. is supported in part by NSF grant DMS-0968879.",

year = "2013",

month = may,

doi = "10.1007/s00220-012-1624-7",

language = "الإنجليزيّة",

volume = "319",

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journal = "Communications in Mathematical Physics",

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T1 - Limit Theorems for Self-Similar Tilings

AU - Bufetov, Alexander I.

AU - Solomyak, Boris

N1 - Funding Information: 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. Funding Information: B. S. is supported in part by NSF grant DMS-0968879.

PY - 2013/5

Y1 - 2013/5

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-012-1624-7

DO - 10.1007/s00220-012-1624-7

M3 - مقالة

SN - 0010-3616

VL - 319

SP - 761

EP - 789

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Limit Theorems for Self-Similar Tilings

Abstract

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