On the hausdorff dimension of bernoulli convolutions
Akiyama, Shigeki ; Feng, De Jun ; Kempton, Tom and Persson, Tomas LU
(2020)
In International Mathematics Research Notices
2020(19).
p.6569-6595
- Abstract
We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli convolution νβ to arbitrary given accuracy whenever β is algebraic. In particular, if the Garsia entropy H(β) is not equal to log(β) then we have a finite time algorithm to determine whether or not dimH(νβ) = 1.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/634291d5-0f44-44d3-8a7f-b5605cc9a00b
- author
- Akiyama, Shigeki
; Feng, De Jun
; Kempton, Tom
and Persson, Tomas
LU
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- in
- International Mathematics Research Notices
- volume
- 2020
- issue
- 19
- pages
- 27 pages
- publisher
- Oxford University Press
- external identifiers
-
- scopus:85102066780
- ISSN
- 1073-7928
- DOI
- 10.1093/IMRN/RNY209
- language
- English
- LU publication?
- yes
- id
- 634291d5-0f44-44d3-8a7f-b5605cc9a00b
- alternative location
- https://arxiv.org/abs/1801.07118
- date added to LUP
- 2021-03-23 07:01:39
- date last changed
- 2022-04-27 00:53:56
@article{634291d5-0f44-44d3-8a7f-b5605cc9a00b,
abstract = {{<p>We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli convolution νβ to arbitrary given accuracy whenever β is algebraic. In particular, if the Garsia entropy H(β) is not equal to log(β) then we have a finite time algorithm to determine whether or not dimH(νβ) = 1. </p>}},
author = {{Akiyama, Shigeki and Feng, De Jun and Kempton, Tom and Persson, Tomas}},
issn = {{1073-7928}},
language = {{eng}},
number = {{19}},
pages = {{6569--6595}},
publisher = {{Oxford University Press}},
series = {{International Mathematics Research Notices}},
title = {{On the hausdorff dimension of bernoulli convolutions}},
url = {{http://dx.doi.org/10.1093/IMRN/RNY209}},
doi = {{10.1093/IMRN/RNY209}},
volume = {{2020}},
year = {{2020}},
}