Entropy of Bernoulli convolutions and uniform exponential growth for linear groups
| cam.issuedOnline | 2020-04-20 | |
| cam.orpheus.counter | 9 | |
| cam.orpheus.success | Tue May 26 08:17:26 BST 2020 - Embargo updated | |
| dc.contributor.author | Breuillard, E | |
| dc.contributor.author | Varjú, PP | |
| dc.date.accessioned | 2019-01-11T00:31:21Z | |
| dc.date.available | 2019-01-11T00:31:21Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | The exponential growth rate of non polynomially growing subgroups of $GL_d$ is conjectured to admit a uniform lower bound. This is known for non-amenable subgroups, while for amenable subgroups it is known to imply the Lehmer conjecture from number theory. In this note, we show that it is equivalent to the Lehmer conjecture. This is done by establishing a lower bound for the entropy of the random walk on the semigroup generated by the maps $x\mapsto \lambda\cdot x\pm 1$, where $\lambda$ is an algebraic number. We give a bound in terms of the Mahler measure of $\lambda$. We also derive a bound on the dimension of Bernoulli convolutions. | |
| dc.description.sponsorship | Simons Foundation Royal Society ERC | |
| dc.identifier.doi | 10.17863/CAM.35131 | |
| dc.identifier.eissn | 1565-8538 | |
| dc.identifier.issn | 0021-7670 | |
| dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/287816 | |
| dc.language.iso | eng | |
| dc.publisher | Springer Science and Business Media LLC | |
| dc.publisher.url | http://dx.doi.org/10.1007/s11854-020-0100-0 | |
| dc.subject | math.CA | |
| dc.subject | math.CA | |
| dc.subject | math.GR | |
| dc.subject | math.PR | |
| dc.title | Entropy of Bernoulli convolutions and uniform exponential growth for linear groups | |
| dc.type | Article | |
| dcterms.dateAccepted | 2018-06-10 | |
| prism.endingPage | 481 | |
| prism.issueIdentifier | 2 | |
| prism.publicationDate | 2020 | |
| prism.publicationName | Journal d'Analyse Mathematique | |
| prism.startingPage | 443 | |
| prism.volume | 140 | |
| pubs.funder-project-id | Royal Society (UF140146) | |
| pubs.funder-project-id | Simons Foundation (LETTER DATED 10-NOV-09) | |
| rioxxterms.licenseref.startdate | 2020-03-01 | |
| rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
| rioxxterms.type | Journal Article/Review | |
| rioxxterms.version | AM | |
| rioxxterms.versionofrecord | 10.1007/s11854-020-0100-0 |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- 1510.04043v3.pdf
- Size:
- 382.32 KB
- Format:
- Adobe Portable Document Format
- Description:
- Accepted version
- Licence
- http://www.rioxx.net/licenses/all-rights-reserved
License bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- DepositLicenceAgreement.pdf
- Size:
- 417.78 KB
- Format:
- Adobe Portable Document Format