PhD Thesis: "Continuité,
moments d'ordres
négatifs, et analyse multifractale des cascades
multiplicatives de
Mandelbrot", Thèse de l'Université Paris Sud,
numéro
d'ordre 4704, 1997.
Habilitation
Thesis: "Analyse
multifractale de processus multiplicatifs ou additifs et
ubiquité conditionnée", 2005 pdf.
Notes
J.
Barral:
Une variante des martingales de B. Mandelbrot, C. R. Acad. Sci. Paris,
324, Série I, 1997, 93--98 (self-contained).
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 and 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
and S.
Seuret: Sums of Dirac masses and conditioned ubiquity, C. R.
Acad. Sci. Paris, Ser. I, 339 (2004), 787--792, pdf.
J. Barral and S. Seuret: Wavelet series built using multifractal
measures. C. R. Math. Acad. Sci. Paris 341 (2005), no. 6, 353--356, pdf.
J. Barral and 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, 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).
Papers (some of them are available on arXiv)
J.
Barral: Moments, continuité, et analyse multifractale des
martingales de Mandelbrot, Probab. Theory
Relat. Fields, 113 (1999),
535--569.
J. Barral: Continuity of the multifractal spectrum of a random
statistically self-similar measure, J. Theoretic. Probab., 13 (2000),
1027--1060, 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: Generalized vector multiplicative cascades, Adv. Appl.
Prob., 33 (2001), 874--895, pdf.
J. Barral and B.
Mandelbrot: Multifractal products of cylindrical pulses,
Probab. Theory Relat. Fields, 124 (2002), 409--430, pdf.
J. Barral: Poissonian products of random weights: Uniform
convergence and related measures, Rev. Mat. Iberoamericana, 19 (2003),
1--44, 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, M.-O.
Coppens and B. Mandelbrot: Multiperiodic multifractal martingales measures, J.
Math. Pures Appl., 82 (2003), 1555--1589, pdf.
J. Barral and 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 2, pp 3--16. AMS, Providence,
RI (2004), pdf.
J. Barral and 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 2. AMS, Providence, RI (2004), pdf.
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 and 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 and S. Seuret: Functions with multifractal variations,
Math. Nachr., 274--275 (2004), 3--18, pdf.
J. Barral and S. Seuret: Combining multifractal additive and
multiplicative chaos, Commun. Math. Phys., 257 (2005),
473--497, pdf.
J. Barral and S. Seuret: Inside singularity sets of
random Gibbs measures, J. Stat. Phys., 120 (2005), 1101--1124, pdf.
J. Barral and S. Seuret: From multifractal measures to
multifractal wavelet series, J. Fourier Anal. Appl., 11 (2005),
589--614, pdf.
J. Barral and A.H. Fan: Covering numbers of different points in
Dvoretzky covering, Bull. Sci. Math., 129 (2005), 275-317, pdf.
J. Barral and S. Seuret: Renewal of singularity sets of random
self-similar measures, Adv. Appl. Probab., 39 (2007), 162--188, pdf.
J. Barral and S. Seuret: Information parameters and large
deviation spectrum of discontinuous measures, Real Analysis Exchanges,
32 (2007) pdf.
J. Barral and M. Mensi: Gibbs measures on self-affine Sierpinski
carpets and their singularity spectrum, Ergod. Th. & Dynam.
Sys., 27 (2007), 1419--1443, pdf.
J. Barral and S. Seuret: Threshold ans Hausdorff spectrum of
discontinous measures, Real Analysis Exchanges, 32 (2007), pdf.
J. Barral and S. Seuret: The singularity spectrum of
Lévy processes in multifractal time, Adv. Math,
214 (2007), 437--468, pdf.
J. Barral and S. Seuret: Heterogeneous ubiquitous
systems in R^d and Hausdorff dimension, Bull.
Braz. Math. Soc., 38 (2007), 476--515. pdf.
J. Barral and S. Seuret: Ubiquity and large intersection
properties under digit frequencies constraints, Math. Proc.
Cambridge Phil. Soc., 145 (2008), 527--548.pdf.
J. Barral and S. Seuret: The multifractal nature of heterogeneous
sums of Dirac masses, Math. Proc. Cambridge Phil. Soc., 144 (2008),
707--727. pdf.
J. Barral, J. Peyrière and Z.-Y. Wen: Dynamics of
Mandelbrot cascades, Probab. Theory Rel. Fields, 144 (2009), 615--631, pdf.
J. Barral, B. Mandelbrot: Fractional multiplicative
processes, Ann. Inst. H. Poincaré Probab. &
Stat., 45
(2009), 1116--1129.
J.
Barral et S. Seuret, The singularity spectrum of the inverse of
cookie-cutters, Ergod. Th. & Dynam. Sys., (2009) 29
(4) 1075-1095, pdf.
J. Barral, D.-J.
Feng: Weighted thermodynamic formalism and
applications, arXiv:0909.4247.
J. Barral, X. Jin and B. Mandelbrot: Uniform convergence for
complex [0,1]-martingales, Ann. Appl. Probab., 20
(2010), 1205--1218.
J. Barral, X. Jin and B. Mandelbrot: Convergence of signed
multiplicative cascades, Ann. Appl. Probab., 20 (2010),
1219-1252.
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: Multifractal analysis for complex random
cascades, Commun. Math. Phys., 219 (2010), 129--168.
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, 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, Y.-H. Qu: Multifractals in Weyl asymptotic distribution, Nonlinearity,
24 (2011), 2785--2012.
J. Barral, P. Loiseau: Large deviations for the local behavior of random walks,
Stoch.
Proc. Appl., 121 (2011), 2272-2302.
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, D.-J. Feng: Multifractal
formalism for almost all self-affine measures, Commun. Math. Phys., 318 (2013),
473-504, arXiv:1110.6578.
J. Barral, X. Jin, R. Rhodes, V. Vargas: Gaussian multiplicative chaos and KPZ duality,
Commun. Math. Phys., 323(2)
(2013), 451-485.
J. Barral, A. Kupiainen, M.
Nikula, E. Saksman, C. Webb: Critical Mandelbrot cascades, Commun. Math. Phys, 325 (2014), 685-711.
J. Barral, X. Jin: On exact scaling
log-infinitely divisible cascades, to appear in Probab. Theory Relat.
Fields.
J. Barral, A. Kupiainen, M.
Nikula, E. Saksman, C. Webb: Basic properties of critical lognormal
multiplicative cascades, arXiv:1206.5444, to appear in Ann. Probab.
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.
J.
Barral: Inverse problems in multifractal analysis of measures, to appear in Ann. Sci. Ec. Norm. Sup.
J. Barral, J. Peyrière: Mandelbrot
cascades on random weighted trees and nonlinear smoothing transforms, submitted.
J. Barral, Y. Hu, T. Madaule: The minimum of a branching random walk outside the boundary case, submitted.
Papers on applied maths
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. Based on paper [36].
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.
Conferences proceedings
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: Mandelbrot cascades and related topics, in "Geometry
and Analysis of Fractals", Hong-Kong 2012, Springer Proceedings in
Mathematics and Statistics, vol. 88, 2014.
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», help 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.