Sixty Years of Bernoulli Convolutions

By Yuval Peres, Wilhelm Schlag, Boris Solomyak. 2000

341 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1bad9643c6e6f9e36c4cd34c9b1cfe1bdb6ecb10

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Citations in the corpus

The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers (2005, background): “The limited Rademacher functions and Bernoulli convolutions have been studied for a long time, revealing many connections with harmonic analysis, number theory, fractal geometry and dynamical systems, see [1,30,48,53,57].”
Weak convergence and spectrality of infinite convolutions (2022, background): “Readers can refer to the excellent survey paper [46] for this topic.”
Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L2-Wavelet Generators with Fractional Scales (2015, background): “For some of the fundamentals in the theory of Bernoulli convolutions, we refer to [30, 42, 43].”
Absolute continuity of self-similar measures, their projections and convolutions (2014, result): “the set of parameters usuch that µu has no power Fourier decay (µu R D1q has zero Hausdorﬀ dimension. The arguments have many points in common with the original proof of Erd˝os-Kahane as presented in [21], but each of them has its own peculiarities. 3.2. Families of self-similar measures with varyin”
Local entropy averages and projections of fractal measures (2009, background): “See [28] and references therein for further background.”
On the modulus of continuity for spectral measures in substitution dynamics (2013, methodology): “The survey [33] contains a detailed exposition of these results (Erdős’ Theorem with Kahane’s improvement) with quantitative estimates.”
Developments in fractal geometry (2013, neutral): “Bandt also noted a relationship between M and Bernoulli convolutions, reviewed in [103].”
On the dimension of Bernoulli convolutions for all transcendental parameters (2018, background): “Instead, we refer the interested readers to the surveys [11, 14, 21, 22].”
Absolute continuity of Bernoulli convolutions for algebraic parameters (2016, neutral): “For thorough surveys on Bernoulli convolutions we refer to [19] and [23].”
Recent progress on Bernoulli convolutions (2016, background): “For the details we refer to the original papers and the survey [48], which treats the topic extensively.”
Canonical number systems, counting automata and fractals (2002, background): “The problem of determining the Hausdorff dimension of self affine sets is strongly related to the behaviour of infinite Bernoulli convolutions (we refer to the excellent survey paper [36] by Peres, Schlag and Solomyak, where interesting references are given).”
On self-similar sets with overlaps and inverse theorems for entropy (2012, background): “e continuity but little more seems to be known about this question except the relatively soft fact that the set of parameters with dimνλ = 1 is also topologically large (contains a dense Gδ set); see [25]. In particular the only parameters λ ∈ [1/2,1) for which dimνλ < 1 is known are inverses of ”