Publikationen
University of Zürich - open access archive
mathscinet
hal - preprints
Books
J. Bertoin, N. Curien, A. Riera (2024). Self-similar Markov trees and scaling limits to appear in IMS Monographs, Cambridge University Press [arxiv]
J. Bertoin (2006). Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics 102 Cambridge University Press, 2006
J. Bertoin (1996). Lévy Processes. Cambridge Tracts in Mathematics 121 Cambridge University Press, 1996 (2nd edition 1998)
Publications since 1999
J. Bertoin, A. Riera, A. Rosales-Ortiz (2026). Local times and excursions for self-similar Markov trees [arxiv]
J. Bertoin, B. Mallein (2025). Reinforced Galton-Watson processes III: Empirical offspring distributions. Probability Theory and Related Fields (2025)
J. Bertoin (2025). On a population model with memory. Bernoulli [arxiv]
J. Bertoin, B. Mallein (2025). Reinforced Galton-Watson processes II: Large time behaviors. Ann. Appl. Probab. 35 (2025), no. 2, 1353–1372. [arxiv]
J. Bertoin, B. Mallein (2023). Reinforced Galton-Watson processes I: Malthusian exponents. Random Structures & Algorithms, first published: 22 April 2024 [arxiv]
J. Bertoin (2023). A model for an epidemic with contact tracing and cluster isolation, and a detection paradox. J. Appl. Probab. 60 (2023), no. 3, 1079–1095.
J. Bertoin (2023). Limits of Pólya urns with innovations . Electron. J. Probab. 28: 1-19 (2023)
J. Bertoin (2021). On the local times of noise reinforced Bessel processes. Annales Henri Lebesgue, Volume 5 (2022), pp. 1277-1294.
J. Bertoin (2021). Counting the zeros of an elephant random walk. Trans. Amer. Math. Soc. 375 (2022), 5539-5560. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Article electronically published on March 31, 2022 [arxiv]
J. Bertoin, H. Yang (2021). Scaling limits of branching random walks and branching stable processes. J. Appl. Probab. 59.4, 2022
J. Bertoin (2021). Counterbalancing steps at random in a random walk. J. Eur. Math. Soc. (JEMS), 1 - 23, 2023, online first . doi: 10.4171/JEMS/1403 [arxiv]
E. Baur, J. Bertoin (2021). On a two-parameter Yule-Simon distribution. In: Chaumont, L., Kyprianou, A.E. (eds) A Lifetime of Excursions Through Random Walks and Lévy Processes. Progress in Probability, vol 78. Birkhäuser, Cham, 2022 [arxiv]
J. Bertoin, N. Curien, I. Kortchemski (2019). On conditioning a self-similar growth-fragmentation by its intrinsic area. Ann. Inst. H. Poincaré Probab. Statist. 57(2), 1136 - 1156, 2021 [arxiv]
J. Bertoin. Scaling exponents of step-reinforced random walks . Probab. Theory Relat. Fields, 179, 295–315, 2021 [link]
J. Bertoin (2019). Universality of Noise Reinforced Brownian Motions. In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, 2021 [link]
J. Bertoin (2020). How linear reinforcement affects Donsker's theorem for empirical processes. Probab. Theory Relat. Fields, 2020
J. Bertoin (2020). Noise reinforcement for Lévy processes. Annales de l’Institut Henri Poincaré, Probab. Statist., vol 56-3, 2236 - 2252, 2020 [link]
J. Bertoin, A. Watson (2020). The strong Malthusian behavior of growth-fragmentation processes. Annales Henri Lebesgue, 3, 795 - 823, 2020 [arxiv]
J. Bertoin (2019). A version of Herbert A. Simon's model with slowly fading memory and its connections to branching processes. Journal of Statistical Physics, pp 1–13, 2019 [arxiv]
J. Bertoin (2018). On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. Journal of Functional Analysis, available online June 2019 [link]
J. Bertoin, B. Mallein (2017). Infinitely ramified point measures and branching Lévy processes. Ann. Probab., 47 - 3, 1619 - 1652, 2019 [arxiv]
J. Bertoin (2018). Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Lévy processes. Stochastic Processes and their Applications, vol. 129-4, 1443-1454, 2019 [arxiv]
J. Bertoin, A. Cortines Peixoto, B. Mallein (2018). Branching-stable point measures and processes. Advances in Applied Probability, vol. 50-4, 1294-1314, 2018 [arxiv]
J. Bertoin, B. Mallein (2018). Biggins' Martingale Convergence for Branching Lévy Processes. Electron. Commun. Probab. 23, paper no. 83, 2018 [arxiv]
J. Bertoin, N. Curien, I. Kortchemski (2018). Random planar maps & growth-fragmentations. Annals of Probability, vol. 46-1, 207-260, 2018 [arxiv]
J. Bertoin, A. Watson (2017). A probabilistic approach to spectral analysis of growth-fragmentation equations. Journal of Functional Analysis, 274, 8, 2163-2204, 2018 [arxiv]
J. Bertoin, T. Budd, N. Curien, I. Kortchemski. Martingales in self-similar growth-fragmentations and their connections with random planar maps. Probability Theory and Related Fields, 1-62, 2017 [arxiv]
E. Baur, J. Bertoin (2017). Weak limits for the largest subpopulations in Yule processes with high mutation probabilities. Advances in Applied Probability 49-3, 877-902, 2017 [arxiv]
J. Bertoin (2015). Markovian growth-fragmentation processes. Bernoulli 23, 1082-1101, 2017 [link]
E. Baur, J. Bertoin (2016). Sur la destruction de grands arbres aléatoires récursifs. Gazette des mathématiciens, vol. 150, 41-47, 2016
E. Baur, J. Bertoin (2016). Elephant Random Walks and their connection to Pólya-type urns. Phys. Rev. E, vol. 94-5, 052134, 2016
J. Bertoin (2016). Mathematical Models for Population Dynamics: Randomness versus Determinism . Mathematics and Society, EMS Publishing House, 81 - 99, 2016
J. Bertoin, R. Stephenson. Local explosion in self-similar growth-fragmentation processes. Electron. Commun. Probab. , vol. 21, 21 - 66, 2016 [arxiv]
J. Bertoin, A. Watson (2016). Probabilistic aspects of critical growth-fragmentation equations. Advances in Applied Probability, vol. 48, Issue A, 37 - 61, July 2016 [arxiv]
J. Bertoin, I. Kortchemski (2015). Self-similar scaling limits of Markov chains on the positive integers . Ann. Appl. Probab 26, 2556-2595, 2016
J. Bertoin (2015). Marc Yor et les temps locaux Marc Yor - La passion du mouvement brownien. Numéro spécial Gazette des Mathématiciens - Matapli, 25-38, 2015
E. Baur, J. Bertoin (2014). The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes. Electron. J. Probab. 20, no. 98, 1-20, 2015
J. Bertoin (2013). The cut-tree of large recursive trees. Annales de l’Institut Henri Poincaré 51, 478 - 488, 2015
J. Bertoin (2015). Compensated fragmentation processes and limits of dilated fragmentations . Ann. Probab. 44, 1254-1284, 2016
J. Bertoin, G. Uribe Bravo (2012). Supercritical percolation on large scale-free random trees. Annals of Applied Probability, vol. 25-1, 81 - 130, 2015
E. Baur, J. Bertoin (2014). Cutting edges at random in large recursive trees . Stochastic Analysis and Applications, Springer, 51 - 76, 2014
J. Bertoin, M. Yor (2013). Local times for functions with finite variation: two versions of Stieltjes change of variables formula. Bull. London Math. Soc. 46, 553 - 560, 2014
J. Bertoin (2013). On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. Electron. J. Probab. 19, No 24, 2014
J. Bertoin (2013). Hoy día, ¿podemos confiar en la estadística?. Crónica.com.mx, Nov. 2013
J. Bertoin, M. Yor (2013). Pure jump increasing processes and the change of variables formula. Electron. Commun. Probab. 18, No. 4, 2013
J. Bertoin (2012). Paul Lévy et l'arithmétique des lois de probabilités. ESAIM Probability and Statistics 17, 790 - 794, 2013
J. Bertoin (2013). Almost giant clusters for percolation on large trees with logarithmic heights. J. Appl. Prob. 50, 603 - 611, 2013
J. Bertoin (2013). On largest offsprings in a critical branching process with finite variance. J. Appl. Prob. 50, 791 - 800, 2013
J. Bertoin, G. Miermont (2013). The cut-tree of large Galton-Watson trees and the Brownian CRT. Ann. Appl. Probab. 23, 1469 - 1493, 2013
J. Bertoin, D. Dufresne, M. Yor (2012). Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion. Rev. Mat. Iberoam. 29, 4, 1307 - 1324, 2013
J. Bertoin (2014). Sizes of the largest clusters for supercritical percolation on random recursive trees. Random Struct. Alg. 44, 29 – 44, 2014
J. Bertoin, M. Yor (2011). Retrieving information from subordination. Prokhorov and Contemporary Probability Theory Eds: Albert N. Shiryaev, S. R. S. Varadhan, Ernst L. Presman Springer, 97 - 106, 2013.
J. Bertoin (2012). Coagulation with limited aggregations. European Congress of Mathematics, EMS, 195 - 209, 2012
J. Bertoin (2012). The area of a self-similar fragmentation. Alea, Volume IX, 53 - 66, 2012
J. Bertoin (2012). Fires on trees. Annales de l'Institut Henri Poincaré Probabilités et Statistiques 48(4), 909 - 921, 2012
J. Bertoin, M. Barczy (2011). Functional limit theorems for Lévy processes satisfying Cramér's condition. Electronic J. of Probability 16, 2020 - 2038, 2011
J. Bertoin (2011). On the maximal offspring in a critical branching process with infinite mean. J. Appl. Probab. 48, 576 - 582, 2011
J. Bertoin (2011). Burning cars in a parking lot. Commun. Math. Phys. 306, 261 - 290, 2011
J. Bertoin (2011). Some applications of duality for Lévy processes in a half-line. Bull. London Math. Soc. 43, 97 - 110, 2011
J. Bertoin, J. Berestycki, B. Haas, G. Miermont (2010). Quelques aspects fractals des processus de fragmentation aléatoire. Quelques interactions entre analyse, probabilités et fractals
Panorama et Synthèses 32, 191 - 243, 2010
J. Bertoin (2010). Asymptotic regimes for the partition into colonies of a branching process with emigration. Ann. Appl. Probab. 20, 1967 - 1988, 2010
J. Bertoin (2010). A two-time-scale phenomenon for a fragmentation-coagulation process. Electron. Commun. Probab. 15, 253 - 262, 2010
J. Bertoin (2010). A limit theorem for trees of alleles in branching processes with rare neutral mutations
A tribute to Kiyosi Itô. Stochastic Process. Appl. 120, 678 - 697, 2010
J. Bertoin, V. Sidoravicius, M.E. Vares (2010). A system of grabbing particles related to Galton-Watson trees. Random Structures Algorithms 36, 477 - 487, 2010
J. Bertoin (2009). Two solvable systems of coagulation equations with limited aggregations. Ann. Inst. Henri Poincaré 26, 2073 - 2089, 2009
J. Bertoin (2009). The structure of the allelic partition of the total population
for Galton-Watson processes with neutral mutations. Ann. Probab. 37, 1502 - 1523, 2009
J. Bertoin, V. Sidoravicius (2009). The structure of typical clusters in large sparse random configurations. J. Stat. Phys. 235, 87 - 105, 2009
J. Bertoin, J. Fontbona, S. Martinez (2008). On prolific individuals in a supercritical continuous state branching process. J. Appl. Probab. 45, 714 - 726
J. Bertoin (2008). Asymptotic regimes for the occupancy scheme of multiplicative escades. Stochastic Process. Appl. 118, 1586 - 1605, 2008
J. Bertoin (2008). Multitype homogeneous fragmentations. In and Out of Equilibrium 2
Eds. V. Sidoravicius and M.E. Vares
Progress in Probability, 161 - 183, 2008
J. Bertoin (2008). A second order SDE for the Langevin process reflected at a completely inelastic boundary. J. Euro. Math. Soc 10, 625 - 639, 2008
J. Bertoin, A. Lindner, R. Maller (2008). On continuity properties of the law of integrals of Lévy processes. Séminaire de Probabilités XLI
Lecture Notes in Mathematics 1934, 137 - 159, Springer 2008
J. Bertoin (2008). Two-parameter Poisson-Dirichlet measures and reversible
exchangeable fragmentation-coalescence processes. Combin. Probab. Comp. 17, 329 - 337, 2008
J. Bertoin, R. Doney, R. Maller (2008). Passage of Lévy processes across power law boundaries at small times. Ann. Probab. 36, 160 - 197, 2008
J. Bertoin (2007). Reflecting a Langevin process at an absorbing boundary. Ann. Probab. 35, 2021 - 2037, 2007
J. Bertoin, T. Fujita, B. Roynette, M. Yor (2006). On a particular class of self-decomposable random variables: the duration
of a Bessel excursion straddling independent exponential times. Probab. Math. Stat 26, 315 - 366, 2006
J. Bertoin, J.-F. Le Gall (2006). Stochastic flows associated to coalescent processes III: Limits theorems. Illinois J. Math. 50, 147 - 181, 2006
J. Bertoin, G. Miermont (2006). Asymptotics in Knuth's parking problem for caravans. Random Structures Algorithms 29, 38 - 55, 2006
J. Bertoin (2006). Some aspects of a random fragmentation model. Stochastic Process. Appl. 116, 345 - 369, 2006
J. Bertoin, M. Yor (2005). Exponential functionals of Lévy processes. Probability Survey 2, 191 - 212, 2005
J. Bertoin. SLE et invariance conforme (d'après Lawler, Schramm et Werner). Séminaire Bourbaki, Volume 2003/2004
Astérisque 299, 15 - 28, 2005
J. Bertoin, J.-F. Le Gall (2005). Stochastic flows associated to coalescent processes II:
Stochastic differential equation. Ann. Inst. Henri Poincaré 41, 307 - 333, 2005
J. Bertoin, S. Martinez (2005). Fragmentation energy. Adv. Appl. Probab. 37, 553 - 570, 2005
J. Bertoin, A. Rouault (2005). Discretization methods for homogeneous fragmentations. J. London Math. Soc. 72, 91 - 109, 2005
J. Bertoin, Ph. Biane, M. Yor (2004). Poissonian exponential functionals, q-series, q-integrals,
and the moment problem for log-normal distributions. Seminar on Stochastic Analysis, Random Fields and Applications IV
Eds. R. Dalang, M. Dozzi, F. Russo
Progress in Probability 58, 45 - 56, Birkhäuser, 2004
J. Bertoin, C. Goldschmidt (2004). Dual random fragmentation and coagulation and an application
to the genealogy of Yule processes. Mathematics and Computer Science III: Algorithms, Trees,Combinatorics and Probabilities
Eds. M. Drmota, P. Flajolet, D. Gardy, B. Gitttenberger
295 - 308, Birkhäuser, 2004
J. Bertoin, A. Gnedin (2004). Asymptotic laws for nonconservative self-similar fragmentations. Electron. J. Probab. 9, 575 - 593, 2004
J. Bertoin (2004). Random covering of an interval and a variation of Kingman's coalescent. Random Structures Algorithms 25, 277 -292, 2004
J. Bertoin (2004). Some aspects of random fragmentations in continuous times. Dynamics and Randomness II
Eds. A. Maass, S. Martinez, S. San Martin
Kluwer, 1 - 15, 2004
J. Bertoin (2004). On small masses in self-similar fragmentations. Stochastic Process. Appl. 109, 13 - 22, 2004
J. Bertoin, L. Chaumont, J. Pitman (2003). Path transformations of first passage bridges. Electron. Commun. Probab. 8, 155 - 166, 2003
J. Bertoin (2003). The asymptotic behavior of fragmentation processes. J. Euro. Math. Soc 5, 395 - 416, 2003
J. Bertoin, J.-F. Le Gall (2003). Stochastic flows associated to coalescent processes. Probab. Theory Relat. Fields 126, 261 - 288, 2003
J. Bertoin, M. Yor (2002). On the entire moments of self-similar Markov processes and exponential functionals
of certain Lévy processes. Ann. Fac. Sci. Toulouse Série 6, vol. XI, 33 - 45, 2002
J. Bertoin (2002). Self-attracting Poisson clouds in an expanding universe. Commun. Math. Phys. 232, 59 - 81, 2002
J. Bertoin (2002). Some aspects of additive coalescents. Proceedings ICM 2002 vol. III, Higher Education Press, 15 - 23, 2002
J. Bertoin (2002). Eternal solutions to Smoluchowski's coagulation equation with additive kernel
and their probabilistic interpretations. Ann. Appl. Probab. 12, 547 - 564, 2002
J. Bertoin, M. Yor (2002). Entrance laws of self-similar Markov processes and
exponential functionals of Lévy processes. Potential Analysis 17, 389 - 400, 2002
J. Bertoin, M.-E. Caballero (2002). Entrance from 0+ for increasing semi-stable Markov processes. Bernoulli 8, 195 - 205, 2002
J. Bertoin (2002). Self-similar fragmentations. Ann. Inst. Henri Poincaré 38, 319 - 340, 2002
J. Bertoin, M. Yor (2001). On subordinators, self-similar Markov processes, and some factorizations
of the exponential law. Electron. Commun. in Probab. 6, 95 - 106, 2001
J. Bertoin, C. Giraud, Y. Isozaki (2001). Statistics of a flux in Burgers turbulence with one-sided Brownian initial data. Commun. Math. Phys. 224, 551 - 564, 2001
J. Bertoin (2001). Homogeneous fragmentation processes. Probab. Theory Relat. Fields 121, 301 -318, 2001
J. Bertoin (2001). Eternal additive coalescents and certain bridges with exchangeable increments. Ann. Probab. 29, 344 - 360, 2001
J. Bertoin (2001). Some properties of Burgers turbulence with white or stable noise initial data. Eds. Barndorff-Nielson, Mikosch and Resnick
Lévy processes: theory and aplications, Birkhäuser, 267 - 279, 2001
J. Bertoin (2001). Elements on Lévy processes. Stochastic Processes: Theory and Methods
Handbook of Statistics 19, Elsevier, 117 - 144, 2001
J. Bertoin (2000). A fragmentation process connected to Brownian motion. Probab. Theory Relat. Fields 117, 289 - 301, 2000
J. Bertoin, J.-F. Le Gall (2000). The Bolthausen-Sznitman coalescent and the genealogy of
continuous-state branching processes. Probab. Theory Relat. Fields 117, 249 - 266, 2000
J. Bertoin, J. Pitman (2000). Two coalescents derived from the range of stable subordinators. Electron. J. Probab. 5, 1 - 17, 2000
J. Bertoin (2000). The convex minorant of the Cauchy process. Electron. Commun. in Probab. 5, 51 - 55, 2000
J. Bertoin (2000). Clustering statistics for sticky particles with Brownian initial velocity. J. Math. Pures Appl. 79, 173 - 194, 2000
J. Bertoin (1999). renewal theory for embedded regenerative sets. Ann. Probab. 27, 1523 - 1535, 1999
J. Bertoin (1999). Subordinators: Examples and Applications. Ecole d'été de Probabilités de St-Flour XXVII
Lect. Notes in Maths 1717, Springer, 1 - 91, 1999
J. Bertoin, K. van Harn, F.W. Steutel (1999). Renewal theory and level passage by subordinators. Stat. Probab. Letters 45, 65 - 69, 1999
J. Bertoin (1999). On overshoots and hitting times for random walks. J. Appl. Probab. 36, 593 - 600, 1999
J. Bertoin, J. Pitman, J. Ruiz de Chavez (1999). Construction of a Brownian path with a given minimum. Electron. Commun. in Probab. 4, 31 - 37, 1999
J. Bertoin (1999). Structure of shocks in Burgers turbulence with stable noise initial data. Commun. Math. Phys. 203, 729 - 741, 1999
J. Bertoin (1999). Intersection of independent regenerative sets. Probab. Theory Relat. Fields 114, 97 - 121, 1999
J. Bertoin, M.-E. Caballero (1999). Regularity of the Cauchy principal value of the local times of some Lévy processes. Bull. Sc. math. 123, 47 - 58, 1999