48 citations · 272 across the 33 of their papers we have counts for
37 papers
Variational principles for Hausdorff and packing dimensions of fractal percolation on self-affine sponges
Julien Barral, Guilhem Brunet
We establish variational principles for the Hausdorff and packing dimensions of a class of statistically self-affine sponges, including in particular fractal percolation sets obtai…
Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal formalism
Julien Barral, Stéphane Seuret
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one perfo…
Multifractal analysis and Erdös-Rényi laws of large numbers for branching random walks in
Najmeddine Attia, Julien Barral
We revisit the multifractal analysis of -valued branching random walks averages by considering subsets of full Hausdorff dimension of the standard level sets, over each infin…
Besov spaces in multifractal environment and the Frisch-Parisi conjecture
Julien Barral, Stéphane Seuret
In this article, a solution to the so-called Frisch-Parisi conjecture is brought. This achievement is based on three ingredients developed in this paper. First almost-doubling full…
On the action of multiplicative cascades on measures
Julien Barral, Xiong Jin
We consider the action of Mandelbrot multiplicative cascades on probability measures supported on a symbolic space. For general probability measures, we obtain almost a sharp crite…
On multifractal formalism for self-similar measures with overlaps
Julien Barral, De-Jun Feng
Let be a self-similar measure generated by an IFS of similarities on (). When is dimensional regular (see Definition~1.1), we g…