On the dimension of Bernoulli convolutions for all transcendental parameters

被引：30

作者：

Varju, Peter P. ^{[1
]}

机构：

[1] Univ Cambridge, Ctr Math Sci, Cambridge, England

来源：

ANNALS OF MATHEMATICS | 2019年 / 189卷 / 03期

基金：

欧洲研究理事会;

关键词：

Bernoulli convolution; self-similar measure; dimension of measures; Mahler measure; entropy; SELF-SIMILAR SETS; ABSOLUTE CONTINUITY; FAMILY;

D O I：

10.4007/annals.2019.189.3.9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Bernoulli convolution nu(lambda) with parameter lambda is an element of (0, 1) is the probability measure supported on R that is the law of the random variable Sigma +/-lambda(n), where the +/- are independent fair coin-tosses. We prove that dim nu(lambda) = 1 for all transcendental lambda is an element of (1/2, 1).

引用

页码：1001 / 1011

页数：11

共 23 条

[1]

Akiyama S., 2018, 180107118V1 ARXIV

[2]

Bombieri BG06 Enrico, 2006, New Mathematical Monographs, V4, DOI [10.1017/CBO9780511542879, DOI 10.1017/CBO9780511542879]

[3]

Breuillard E., 2018, J ANAL MATH

[4]

Breuillard E., 2018, ANN PROBAB