Sixty Years of Bernoulli Convolutions

2000 ◽  
pp. 39-65 ◽  
Author(s):  
Yuval Peres ◽  
Wilhelm Schlag ◽  
Boris Solomyak
Keyword(s):  
Bernoulli Convolutions

On the multifractal analysis of Bernoulli convolutions. II. Dimensions

1996 ◽  
Vol 82 (1-2) ◽  
pp. 397-420 ◽  
Author(s):  
François Ledrappier ◽  
Anna Porzio
Keyword(s):  
Multifractal Analysis ◽  
Bernoulli Convolutions

scholarly journals Almost sure absolute continuity of Bernoulli convolutions

2010 ◽  
Vol 46 (3) ◽  
pp. 888-893 ◽  
Author(s):  
Michael Björklund ◽  
Daniel Schnellmann
Keyword(s):  
Absolute Continuity ◽  
Bernoulli Convolutions

scholarly journals Spectrality of infinite Bernoulli convolutions

2015 ◽  
Vol 269 (5) ◽  
pp. 1571-1590 ◽  
Author(s):  
Li-Xiang An ◽  
Xing-Gang He ◽  
Hai-Xiong Li
Keyword(s):  
Bernoulli Convolutions

scholarly journals On the Hausdorff Dimension of Bernoulli Convolutions

2018 ◽  
Vol 2020 (19) ◽  
pp. 6569-6595 ◽  
Author(s):  
Shigeki Akiyama ◽  
De-Jun Feng ◽  
Tom Kempton ◽  
Tomas Persson
Keyword(s):  
Hausdorff Dimension ◽  
Rate Of Convergence ◽  
Finite Time ◽  
Time Algorithm ◽  
Bernoulli Convolution ◽  
Bernoulli Convolutions ◽  
Explicit Rate ◽  
Products Of Matrices

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 $\nu _{\beta }$ to arbitrary given accuracy whenever $\beta $ is algebraic. In particular, if the Garsia entropy $H(\beta )$ is not equal to $\log (\beta )$ then we have a finite time algorithm to determine whether or not $\operatorname{dim_H} (\nu _{\beta })=1$.

Bernoulli convolutions and an intermediate value theorem for entropies ofK-partitions

2002 ◽  
Vol 87 (1) ◽  
pp. 337-367 ◽  
Author(s):  
Elon Lindenstrauss ◽  
Yuval Peres ◽  
Wilhelm Schlag
Keyword(s):  
Intermediate Value Theorem ◽  
Bernoulli Convolutions ◽  
Intermediate Value

Improving Poisson Approximations

1994 ◽  
Vol 8 (4) ◽  
pp. 449-462 ◽  
Author(s):  
Erol A. Peköz ◽  
Sheldon M. Ross
Keyword(s):  
Poisson Distribution ◽  
Error Bounds ◽  
Random Variables ◽  
Urn Models ◽  
Matching Problem ◽  
Bernoulli Convolutions ◽  
Poisson Approximations ◽  
Better Than

Let X1,…, Xn, be indicator random variables, and set We present a method for estimating the distribution of W in settings where W has an approximately Poisson distribution. Our method is shown to yield estimates significantly better than straight Poisson estimates when applied to Bernoulli convolutions, urn models, the circular k of n: F system, and a matching problem. Error bounds are given.

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