Publications (30)
Inverse problems in multifractal analysis
Julien Barral
The minimum of a branching random walk outside the boundary case
Julien Barral, Yueyun Hu, Thomas Madaule
Uniform convergence for complex $[\mathbf{0,1}]$-martingales
Julien Barral, Xiong Jin, Benoît Mandelbrot
Hausdorff and packing spectra, large deviations, and free energy for branching random walks in $\R^d$
Najmeddine Attia, Julien Barral
Random sparse sampling in a Gibbs weighted tree
Julien Barral, Stéphane Seuret
A localized Jarnik-Besicovitch Theorem
Julien Barral, Stephane Seuret
Dynamics of Mandelbrot Cascades
Julien Barral, Jacques Peyriere, Zhi-Ying Wen
Multifractal analysis of complex random cascades
Julien Barral, Xiong Jin
Weighted thermodynamic formalism and applications
Julien Barral, De-Jun Feng
Multifractal analysis and localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
Convergence of complex multiplicative cascades
Julien Barral, Xiong Jin, Beno\^{ı}t Mandelbrot
Fractional multiplicative processes
Julien Barral, Benoit Mandelbrot
Basic properties of critical lognormal multiplicative chaos
Julien Barral, Antti Kupiainen, Miika Nikula +2
Inside singularity sets of random Gibbs measures
Julien Barral, Stephane Seuret
Critical Mandelbrot Cascades
Julien Barral, Antti Kupiainen, Miika Nikula +2
Local Multifractal Analysis
Julien Barral, Arnaud Durand, Stéphane Jaffard +1
Large deviations for the local fluctuations of random walks and new insights into the "randomness" of Pi
Julien Barral, Patrick Loiseau
Bilateral Canonical Cascades: Multiplicative Refinement Paths to Wiener's and Variant Fractional Brownian Limits
Julien Barral, Benoit Mandelbrot
Heterogeneous ubiquitous systems in $\mathbb{R}^{d}$ and Hausdorff dimension
Julien Barral, Stephane Seuret
Limiting laws of supercritical branching random walks
Julien Barral, Rémi Rhodes, Vincent Vargas
Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet
Julien Barral, De-Jun Feng
Multifractal formalism for almost all self-affine measures
Julien Barral, De-Jun Feng
Multifractal analysis of Birkhoff averages on "self-affine" symbolic spaces
Julien Barral, Mounir Mensi
Gaussian multiplicative chaos and KPZ duality
Julien Barral, Xiong Jin, Rémi Rhodes +1
Mandelbrot cascades on random weighted trees and nonlinear smoothing transforms
Julien Barral, Jacques Peyrière
A pure jump Markov process with a random singularity spectrum
Julien Barral, Nicolas Fournier, Stephane Jaffard +1
Renewal of singularity sets of statistically self-similar measures
Julien Barral, Stephane Seuret
Localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
Projections of planar Mandelbrot measures
Julien Barral, De-Jun Feng
On exact scaling log-Infinitely divisible cascades
Julien Barral, Xiong Jin