PhD and Habilitation theses:

"Continuité, moments d'ordres négatifs, et analyse multifractale des cascades multiplicatives de Mandelbrot", Thèse de l'Université Paris Sud, numéro d'ordre 4704, 1997. Advisor: Jacques Peyrière.

"Analyse multifractale de processus multiplicatifs ou additifs et ubiquité conditionnée", 2005 pdf.


Notes to Comptes Rendus de l'Académie des Sciences

J. Barral, R. Rhodes et V. Vargas: Limiting laws of supercritical branching random walks, C. R. Acad. Sci. Paris, Ser. I 350 (2012) 535–538 (self-contained).

J. Barral, S. Seuret: A class of multifractal semi-stable processes including Lévy subordinators and Mandelbrot multiplicative cascades, C. R. Acad. Sci. Paris, Ser. I, 241 (2005), 579-582, pdf.

J. Barral, S. Seuret: Wavelet series built using multifractal measures, C. R. Math. Acad. Sci. Paris 341 (2005), no. 6, 353-356, pdf.

J. Barral, S. Seuret: Sums of Dirac masses and conditioned ubiquity, C. R. Acad. Sci. Paris, Ser. I, 339 (2004), 787-792, pdf.

J. Barral, A.H. Fan: Densities of some Poisson T-martingales and random covering numbers, C. R. Acad. Sci. Paris, Ser. I 338 (2004), 571-574, pdf.

J. Barral: Une extension de l'équation fonctionnelle de B. Mandelbrot, C.R.Acad.Sci. Paris, 326, Série I, 1998, 421-426 (self-contained).

J. Barral: Une variante des martingales de B. Mandelbrot, C. R. Acad. Sci. Paris, 324, Série I, 1997, 93-98 (self-contained).


Papers (most of them are available on arXiv or on this page)

J. Barral, S. Seuret: Besov spaces in multifractal environment and the Frisch-Parisi conjecture, preprint

J. Barral, X. Jin: On the action of multiplicative cascades on measures, accepted for publication in I.R.M.N.

J. Barral, D.-J. Feng: Dimensions of random statistically self-affine Sierpinski sponges in R^k, J. Math. Pures Appl., 149 (2021), 254-303.

J. Barral, D.-J. Feng: On multifractal formalism for self-similar measures with overlaps, Math. Z., 298 (2021), 359-383.

J. Barral, S. Seuret: Random sparse sampling on a Gibbs weighted tree and phase transitions, J. Inst. Math. Jussieu, 19 (2020), 65-116.

J. Barral, D.-J. Feng: Projections of planar Mandelbrot random measures, Adv. Math., 325 (2018), 640-718.

J. Barral, J. Peyrière: Mandelbrot cascades on random weighted trees and nonlinear smoothing transforms, Asian J. Math., 22 (2018), 883-918.

J. Barral, Y. Hu, T. Madaule: The minimum of a branching random walk outside the boundary case, Bernoulli, 24 (2018), 801-841.

J. Barral: Inverse problems in multifractal analysis of measures, Ann. Scient. Ec. Norm. Sup, 48 (2015),1457-1510.

J. Barral, A. Kupiainen, M. Nikula, E. Saksman, C. Webb: Basic properties of critical lognormal multiplicative cascades, Ann. Probab, 43 (2015), 2205--2249.

J. Barral, X. Jin: On exact scaling log-infinitely divisible cascades, Probab. Theory Relat. Fields, 160 (2014), 521-565.

N. Attia, J. Barral: Hausdorff and packing spectra, large deviations and free energy for branching random walks in R^d, Comm. Math. Phys, 331 (2014), 139-187. Erratum, 351 (2017), 873-875.

J. Barral, A. Kupiainen, M. Nikula, E. Saksman, C. Webb: Critical Mandelbrot cascades, Commun. Math. Phys, 325 (2014), 685-711.

J. Barral, D.-J. Feng: Multifractal formalism for almost all self-affine measures, Commun. Math. Phys., 318 (2013), 473-504.

J. Barral, X. Jin, R. Rhodes, V. Vargas: Gaussian multiplicative chaos and KPZ duality, Commun. Math. Phys., 323(2) (2013), 451-485.

J. Barral, Y.-H. Qu: Localized asymptotic behavior for almost additive potentials, Discr. Cont. Dynam. Sys. A, 32 (2012), 717-751.

J. Barral, Y.-H. Qu: On the higher dimensional multifractal analysis, Discr. Cont. Dynam. Sys. A, 32 (2012), 1977-1995.

J. Barral, D.-J. Feng: Weighted thermodynamic formalism on subshifts and applications, Asian J. Math., 16 (2012), 319-352.

J. Barral, I. Bhouri: How projections affect the validity of the multifractal formalism, Ergod. Th. & Dynam. Sys., 31 (2011), 673-701.

J. Barral and S. Seuret: A localized Jarnik-Besicovitch theorem, Adv. Math, 226 (2011), 3191--3215. pdf

J. Barral, D.-J. Feng: Non-uniqueness of ergodic measures with full Hausdorff dimension on Gatzouras-Lalley carpet, Nonlinearity, 24 (2011), 2563-2567.

J. Barral, P. Gonçalvès, On the estimation of the large deviations spectrum, J. Stat. Phys., 144 (2011), 1256-1283.

J. Barral, Y.-H. Qu: Multifractals in Weyl asymptotic distribution, Nonlinearity, 24 (2011), 2785-2812.

J. Barral, P. Loiseau: Large deviations for the local behavior of random walks, Stoch. Proc. Appl., 121 (2011), 2272-2302.

J. Barral, X. Jin: Multifractal analysis for complex random cascades, Commun. Math. Phys., 219 (2010), 129-168.

J. Barral, N. Fournier, S.Jaffard, S. Seuret: A simple jump Markov process with a random singularity spectrum, Ann. Probab., 38 (5)(2010), 1924–1946.

J. Barral, X. Jin and B. Mandelbrot: Convergence of signed multiplicative cascades, Ann. Appl. Probab., 20 (2010), 1219-1252.

J. Barral, X. Jin and B. Mandelbrot: Uniform convergence for complex [0,1]-martingales, Ann. Appl. Probab., 20 (2010), 1205-1218.

J. Barral, D.-J. Feng: Weighted thermodynamic formalism and applications, arXiv:0909.4247.

J. Barral, S. Seuret, The singularity spectrum of the inverse of cookie-cutters, Ergod. Th. & Dynam. Sys., (2009) 29 (4) 1075-1095, pdf.

J. Barral, B. Mandelbrot: Fractional multiplicative processes, Ann. Inst. H. Poincaré Probab. & Stat., 45 (2009), 1116-1129.

J. Barral, J. Peyrière, Z.-Y. Wen: Dynamics of Mandelbrot cascades, Probab. Theory Relat. Fields, 144 (2009), 615-631, pdf.

J. Barral, M. Mensi: Multifractal analysis of Birkhoff averages on 'self-affine' symbolic spaces, Nonlinearity, 21 (2008), 2409-2425.

J. Barral, S. Seuret: The multifractal nature of heterogeneous sums of Dirac masses, Math. Proc. Cambridge Phil. Soc., 144 (2008), 707-727. pdf.

J. Barral, S. Seuret: Ubiquity and large intersection properties under digit frequencies constraints, Math. Proc. Cambridge Phil. Soc., 145 (2008), 527-548.pdf.

J. Barral, S. Seuret: Heterogeneous ubiquitous systems in R^d and Hausdorff dimension, Bull. Braz. Math. Soc., 38 (2007), 476-515. pdf.

J. Barral, S. Seuret: The singularity spectrum of Lévy processes in multifractal time, Adv. Math, 214 (2007), 437-468, pdf.

J. Barral, S. Seuret: Threshold ans Hausdorff spectrum of discontinous measures, Real Analysis Exchanges, 32 (2007), pdf.

J. Barral, M. Mensi: Gibbs measures on self-affine Sierpinski carpets and their singularity spectrum, Ergod. Th. & Dynam. Sys., 27 (2007), 1419-1443, pdf.

J. Barral, S. Seuret: Information parameters and large deviation spectrum of discontinuous measures, Real Analysis Exchanges, 32 (2007) pdf.

J. Barral, S. Seuret: Renewal of singularity sets of random self-similar measures, Adv. Appl. Probab., 39 (2007), 162-188, pdf.

J. Barral, A.H. Fan: Covering numbers of different points in Dvoretzky covering, Bull. Sci. Math., 129 (2005), 275-317, pdf.

J. Barral, S. Seuret: From multifractal measures to multifractal wavelet series, J. Fourier Anal. Appl., 11 (2005), 589-614, pdf.

J. Barral, S. Seuret: Inside singularity sets of random Gibbs measures, J. Stat. Phys., 120 (2005), 1101-1124, pdf.

J. Barral, S. Seuret: Combining multifractal additive and multiplicative chaos, Commun. Math. Phys., 257 (2005), 473-497, pdf.

J. Barral, S. Seuret: Functions with multifractal variations, Math. Nachr., 274--275 (2004), 3-18, pdf.

J. Barral, J. Lévy-Véhel: Multifractal analysis of a class of additive processes with correlated non-stationary increments, Elec. J. Probab., 9 (2004), 508-543, pdf.

J. Barral, M.-O. Coppens and B. Mandelbrot: Multiperiodic multifractal martingales measures, J. Math. Pures Appl., 82 (2003), 1555-1589, pdf.

J. Barral, F. Ben Nasr and J. Peyrière: Comparing multifractal formalisms: the Neighboring Boxes Conditions, Asian J. Math., 7 (2003), 149-166, pdf.

J. Barral: Poissonian products of random weights: Uniform convergence and related measures, Rev. Mat. Iberoamericana, 19 (2003), 1-44, pdf.

J. Barral, B. Mandelbrot: Multifractal products of cylindrical pulses, Probab. Theory Relat. Fields, 124 (2002), 409-430, pdf.

J. Barral: Generalized vector multiplicative cascades, Adv. Appl. Prob., 33 (2001), 874-895, pdf.

J. Barral: Differentiability of multiplicative processes related to branching random walks, Ann. Inst. H. Poincaré, Probabilités et Statistiques, 36 (2000), 407-417, pdf.

J. Barral: Continuity of the multifractal spectrum of a random statistically self-similar measure, J. Theoretic. Probab., 13 (2000), 1027-1060, pdf.

J. Barral: Moments, continuité, et analyse multifractale des martingales de Mandelbrot, Probab. Theory Relat. Fields, 113 (1999), 535-569.


Some applied maths

P. Loiseau, C. Médigue, P. Gonçalves, N. Attia, S. Seuret, F. Cottin, D. Chemla, M. Sorine, J. Barral: Large deviations estimates for the multiscale analysis of heart rate variability, Physica A 391 (2012) 5658–5671.

Loiseau, P. Gonçalves, J. Barral, P. Vicat-Blanc Primet: Modeling TCP throughput: An elaborated large-deviations-based and its empirical validation, Performance Evaluation 67 (2010) 1030-1043.


Conferences proceedings and surveys

J. Barral: L^q-spectrum of homogeneous self-similar measures and inverse theorem for the decay of Lq -norms under convolutions. After P. Shmerkin, Oberwolfach Report No. 47/2017 on Additive Combinatorics, Entropy, and Fractal Geometry, pp 51-54.

J. Barral: Inverse problems in multifractal analysis, in "Fractals Geometry and Stochastics V", Tabartz 2014, Vol. 70 of the series Progress in Probability pp 261-278, 2015

J. Barral: Mandelbrot cascades and related topics, in "Geometry and Analysis of Fractals", Hong-Kong 2012, Springer Proceedings in Mathematics and Statistics, vol. 88, pp 1-45, 2014

J. Barral, A. Durand, S. Jaffard and S. Seuret: Local multifractal analysis, in: D. Carfi, M.L. Lapidus, E.P.J. Pearse, and M. van Frankenhuijsen, editors, Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics, Contemporary Mathematics, vol. 601, Amer. Math. Soc., Providence, pages 31-64, 2013.

J. Barral, A.-H. Fan et J. Peyrière: « Mesures engendrées par multiplications » (137 pages), in Panoramas et Synthèses (2010), vol 32.: ``Quelques interactions entre analyse, probabilités et fractals''.

J. Barral: Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures, Part III), pp 53-90. In Proc. Symp. in Pures Math., 72, Part 2. AMS, Providence, RI (2004), pdf.

J. Barral, B. Mandelbrot: Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (Random multiplicative multifractal measures, Part II), pp 17-52, In Proc. Symp. Pures Math., 72, Part II. AMS, Providence, RI (2004), pdf.

J. Barral, B. Mandelbrot: Introduction to infinite products of random independent functions (Random multiplicative multifractal measures, Part I), in ``Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot''. M. L. Lapidus and M. van Frankenhuysen eds. Proc. Symp. in Pures Math., 72, Part I, pp 1-16. AMS, Providence, RI (2004), pdf.


Edition of conferences proceedings

« Fractals and Related Fields », held in 2007 at Monastir, Tunisia: « Recent developments in Fractals and related Fields »,
 Julien Barral, Stéphane Seuret, Eds., 2010, Birkhäuser ISBN 978-0-8176-4887-9.

« Fractals and Related Fields II», held in 2011 at Porquerolles, France: "New developments in Fractals and related Fields", Julien Barral, Stéphane Seuret, Editors, 2013, Birkhäuser. ISBN 978-0-8176-8400-6.

« Fractals and Related Fields III», held in 2015 at Porquerolles, France: "Recent developments in Fractals and related Fields", Julien Barral, Stéphane Seuret, Editors, 2017, Birkhäuser. ISBN 978-3-319-57805-7.