2 citations · 5 across the 7 of their papers we have counts for
9 papers
Fast and slow points of Birkhoff sums
Frédéric Bayart, Zoltan Buczolich, Yanick Heurteaux
We investigate the growth rate of the Birkhoff sums , where is a continuous function with zero mean defined on the unit circle $\mathbb T…
Multifractal phenomena and packing dimension
Frédéric Bayart, Yanick Heurteaux
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract s…
An introduction to Mandelbrot cascades
Yanick Heurteaux
In this course, we propose an elementary and self-contained introduction to canonical Mandelbrot random cascades. The multiplicative construction is explained and the necessary and…
On measures driven by Markov chains
Yanick Heurteaux, Andrzej Stos
We study measures on which are driven by a finite Markov chain and which generalize the famous Bernoulli products. We propose a hands-on approach to determine the structure…
On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets
Frédéric Bayart, Yanick Heurteaux
Let be a compact set in $\rd$ with positive Hausdorff dimension. Using a Fractional Brownian Motion, we prove that in a prevalent set of continuous functions on , the Hausdo…
Multifractal analysis of the divergence of Fourier series: the extreme cases
Frédéric Bayart, Yanick Heurteaux
We study the size, in terms of the Hausdorff dimension, of the subsets of such that the Fourier series of a generic function in $L^1(\TT)$, $L^p(\TT)$ or in $\mathcal C…
Boundary multifractal behaviour for harmonic functions in the ball
Frédéric Bayart, Yanick Heurteaux
It is well known that if is a nonnegative harmonic function in the ball of $\RR^{d+1}$ or if is harmonic in the ball with integrable boundary values, then the radial limit…
Multifractal analysis of the divergence of Fourier series
Frédéric Bayart, Yanick Heurteaux
A famous theorem of Carleson says that, given any function $f\in L^p(\TT)$, , its Fourier series converges for almost every . Beside th…
Measures and the Law of the Iterated Logarithm
Imen Bhouri, Yanick Heurteaux
Let m be a unidimensional measure with dimension d. A natural question is to ask if the measure m is comparable with the Hausdorff measure (or the packing measure) in dimension d.…