Displaying similar documents to “Geometric realizations of substitutions”

Symbolic discrepancy and self-similar dynamics

Boris Adamczewski (2004)

Annales de l'Institut Fourier


We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems. ...

Languages under substitutions and balanced words

Alex Heinis (2004)

Journal de Théorie des Nombres de Bordeaux


This paper consists of three parts. In the first part we prove a general theorem on the image of a language K under a substitution, in the second we apply this to the special case when K is the language of balanced words and in the third part we deal with recurrent -words of minimal block growth.

Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger, Gérard Ben Arous, Sandrine Péché (2009)

Annales de l'I.H.P. Probabilités et statistiques


We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in ( (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

Ka-Sing Lau, Jian-Rong Wang, Cho-Ho Chu (1995)

Studia Mathematica


The Choquet-Deny theorem and Deny’s theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the L p -dimension, the L p -density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.