41 research outputs found
Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences
We comment on some recent investigations on the electronic properties of
models associated to the Thue-Morse chain and point out that their conclusions
are in contradiction with rigorously proven theorems and indicate some of the
sources of these misinterpretations. We briefly review and explain the current
status of mathematical results in this field and discuss some conjectures and
open problems.Comment: 15,CPT-94/P.3003,tex,
Some Aspects of Multifractal analysis
The aim of this survey is to present some aspects of multifractal analysis
around the recently developed subject of multiple ergodic averages. Related
topics include dimensions of measures, oriented walks, Riesz products etc
Self-similar sets: projections, sections and percolation
We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.Postprin
Automatic Dirichlet series
Dirichlet series whose coefficients are generated by finite automata define meromorphic functions on the whole complex plane. As consequences, a new proof of Cobham's theorem on the existence of logarithmic frequencies of symbols in automatic sequences is given, and certain infinite products are explicitly computed
Exactly solvable one-dimensional inhomogeneous models
International audienceWe present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. We treat the example of an Ising chain in a varying magnetic field, but our procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models we can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature