On the Gibbs properties of Bernoulli convolutions
نویسندگان
چکیده
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
منابع مشابه
2 N ov 2 00 4 On the Gibbs properties of Bernoulli convolutions related to β - numeration in multinacci bases
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multi-nacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
متن کاملar X iv : m at h / 05 02 27 7 v 1 [ m at h . D S ] 1 3 Fe b 20 05 INFINITE BERNOULLI CONVOLUTIONS AS AFFINE ITERATED FUNCTION SYSTEMS
We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...
متن کامل2 7 Ju l 2 00 6 Infinite products of 2 × 2 matrices and the Gibbs properties of Bernoulli convolutions
Nevertheless the normalized rows of Pn(ω) in general do not converge: suppose for instance that all the matrices in M are positive but do not have the same positive normalized left-eigenvector, let Lk such that LkMk = ρkLk. For any positive matrix M , the normalized rows of MM0 n converge to L0 and the ones of MM1 n to L1. Consequently we can choose the sequence (nk)k∈N sufficiently increasing ...
متن کاملExchangeable, Gibbs and Equilibrium Measures for Markov Subshifts
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
متن کاملDutkay and Palle
We exploit the fact that the classical Bernoulli systems are con-tractive iterated function systems (IFS) of affine type to prove a number of properties of the infinite Bernoulli convolution measures ν λ. We develop and use a new duality notion for affine IFSs. This duality is based on a natural transfer operator R W , and on an associated random walk process Px. We show that the absolute-squar...
متن کامل