Prof. Dr. Jean Bertoin

Publications

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University of Zürich - open access archive

mathscinet

hal - preprints

Books

Jean Bertoin, Nicolas Curien, Armand Riera (2024). Self-similar Markov trees and scaling limits

Jean Bertoin (2006). Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics 102

Jean Bertoin (1996). Lévy Processes. Cambridge Tracts in Mathematics 121

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Publications since 1999

Jean Bertoin, Bastien Mallein (2025). Reinforced Galton-Watson processes III: Empirical offspring distributions

Jean Bertoin (2025). On a population model with memory

Jean Bertoin, Bastien Mallein (2025). Reinforced Galton-Watson processes II: Large time behaviors. to appear in Annals of Applied Probability

Jean Bertoin, Bastien Mallein (2023). Reinforced Galton-Watson processes I: Malthusian exponents. Random Structures & Algorithms, first published: 22 April 2024

Jean Bertoin (2023). A model for an epidemic with contact tracing and cluster isolation, and a detection paradox

Jean Bertoin (2023). Limits of Pólya urns with innovations

Jean Bertoin (2021). On the local times of noise reinforced Bessel processes

Jean 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

Jean Bertoin, Hairuo Yang (2021). Scaling limits of branching random walks and branching stable processes

Jean Bertoin (2021). Counterbalancing steps at random in a random walk. arXiv:2011.14069. 10.4171/JEMS/1403

Erich Baur, Jean Bertoin (2021). On a two-parameter Yule-Simon distribution. arXiv:2001.01486

Jean Bertoin, Nicolas Curien, Igor Kortchemski (2019). On conditioning a self-similar growth-fragmentation by its intrinsic area. arXiv:1908.07830

Jean Bertoin. Scaling exponents of step-reinforced random walks . hal-02480479

Jean Bertoin (2019). Universality of Noise Reinforced Brownian Motions . hal-02341310

Jean Bertoin (2020). How linear reinforcement affects Donsker's theorem for empirical processes

Jean Bertoin (2020). Noise reinforcement for Lévy processes. hal-01898145

Jean Bertoin, Alexander Rhys Watson (2020). The strong Malthusian behavior of growth-fragmentation processes. arXiv:1901.07251

Jean Bertoin (2019). A version of Herbert A. Simon's model with slowly fading memory and its connections to branching processes. arXiv:1901.08311

Jean Bertoin (2018). On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. hal-01764139v2

Jean Bertoin, Bastien Mallein (2017). Infinitely ramified point measures and branching Lévy processes. arXiv:1703.08078

Jean Bertoin (2018). Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Lévy processes. arXiv:1706.08421

Jean Bertoin, Aser Cortines Peixoto, Bastien Mallein (2018). Branching-stable point measures and processes. arXiv:1805.04316

Jean Bertoin, Bastien Mallein (2018). Biggins' Martingale Convergence for Branching Lévy Processes. arXiv:1712.04769

Jean Bertoin, Nicolas Curien, Igor Kortchemski (2018). Random planar maps & growth-fragmentations. arXiv:1507.02265

Jean Bertoin, Alexander Rhys Watson (2017). A probabilistic approach to spectral analysis of growth-fragmentation equations. arXiv:1701.05061

Jean Bertoin, Timothy Budd, Nicolas Curien, Igor Kortchemski. Martingales in self-similar growth-fragmentations and their connections with random planar maps. arXiv:1605.00581

Erich Baur, Jean Bertoin (2017). Weak limits for the largest subpopulations in Yule processes with high mutation probabilities . arXiv:1603.06564

Jean Bertoin (2015). Markovian growth-fragmentation processes. hal-01152370

Erich Baur, Jean Bertoin (2016). Sur la destruction de grands arbres aléatoires récursifs

Erich Baur, Jean Bertoin (2016). Elephant Random Walks and their connection to Pólya-type urns

Jean Bertoin (2016). Mathematical Models for Population Dynamics: Randomness versus Determinism

Jean Bertoin, Robin Stephenson. Local explosion in self-similar growth-fragmentation processes. arXiv:1602.04957

Jean Bertoin, Alexander Rhys Watson (2016). Probabilistic aspects of critical growth-fragmentation equations. arXiv:1506.09187

Jean Bertoin, Igor Kortchemski (2015). Self-similar scaling limits of Markov chains on the positive integers

Jean Bertoin (2015). Marc Yor et les temps locaux
Marc Yor - La passion du mouvement brownien

Erich Baur, Jean Bertoin (2014). The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes

Jean Bertoin (2013). The cut-tree of large recursive trees

Jean Bertoin (2015). Compensated fragmentation processes and limits of dilated fragmentations

Jean Bertoin, Géronimo Uribe Bravo (2012). Supercritical percolation on large scale-free random trees

Erich Baur, Jean Bertoin (2014). Cutting edges at random in large recursive trees

Jean Bertoin, Marc Yor (2013). Local times for functions with finite variation: two versions of Stieltjes change of variables formula

Jean Bertoin (2013). On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees

Jean Bertoin (2013). Hoy día, ¿podemos confiar en la estadística?

Jean Bertoin, Marc Yor (2013). Pure jump increasing processes and the change of variables formula

Jean Bertoin (2012). Paul Lévy et l'arithmétique des lois de probabilités

Jean Bertoin (2013). Almost giant clusters for percolation on large trees with logarithmic heights

Jean Bertoin (2013). On largest offsprings in a critical branching process with finite variance

Jean Bertoin, Grégory Miermont (2013). The cut-tree of large Galton-Watson trees and the Brownian CRT

Jean Bertoin, Daniel Dufresne, Marc Yor (2012). Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion

Jean Bertoin (2014). Sizes of the largest clusters for supercritical percolation on random recursive trees

Jean Bertoin, Marc Yor (2011). Retrieving information from subordination. Prokhorov and Contemporary Probability Theory
Eds: Albert N. Shiryaev, S. R. S. Varadhan, Ernst L. Presman

Jean Bertoin (2012). Coagulation with limited aggregations

Jean Bertoin (2012). The area of a self-similar fragmentation

Jean Bertoin (2012). Fires on trees

Jean Bertoin, Mátyás Barczy (2011). Functional limit theorems for Lévy processes satisfying Cramér's condition. Electronic J. of Probability 16, 2020 - 2038, 2011

Jean Bertoin (2011). On the maximal offspring in a critical branching process with infinite mean. J. Appl. Probab. 48, 576 - 582, 2011

Jean Bertoin (2011). Burning cars in a parking lot. Commun. Math. Phys. 306, 261 - 290, 2011

Jean Bertoin (2011). Some applications of duality for Lévy processes in a half-line. Bull. London Math. Soc. 43, 97 - 110, 2011

Jean Bertoin, Julien Berestycki, Bénédicte Haas, Grégory Miermont (2010). Quelques aspects fractals des processus de fragmentation aléatoire. Quelques interactions entre analyse, probabilités et fractals
Panorama et Synthèses 32, 191 - 243, 2010

Jean Bertoin (2010). Asymptotic regimes for the partition into colonies of a branching process with emigration. Ann. Appl. Probab. 20, 1967 - 1988, 2010

Jean Bertoin (2010). A two-time-scale phenomenon for a fragmentation-coagulation process. Electron. Commun. Probab. 15, 253 - 262, 2010

Jean 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

Jean Bertoin, Vladas Sidoravicius, Maria Eulália Vares (2010). A system of grabbing particles related to Galton-Watson trees. Random Structures Algorithms 36, 477 - 487, 2010

Jean Bertoin (2009). Two solvable systems of coagulation equations with limited aggregations. Ann. Inst. Henri Poincaré 26, 2073 - 2089, 2009

Jean 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

Jean Bertoin, Vladas Sidoravicius (2009). The structure of typical clusters in large sparse random configurations. J. Stat. Phys. 235, 87 - 105, 2009

Jean Bertoin, Joaquin Fontbona, Servet Martinez (2008). On prolific individuals in a supercritical continuous state branching process. J. Appl. Probab. 45, 714 - 726

Jean Bertoin (2008). Asymptotic regimes for the occupancy scheme of multiplicative escades. Stochastic Process. Appl. 118, 1586 - 1605, 2008

Jean Bertoin (2008). Multitype homogeneous fragmentations. In and Out of Equilibrium 2
Eds. V. Sidoravicius and M.E. Vares
Progress in Probability, 161 - 183, 2008

Jean Bertoin (2008). A second order SDE for the Langevin process reflected at a completely inelastic boundary. J. Euro. Math. Soc 10, 625 - 639, 2008

Jean Bertoin, Alexander Lindner, Ross 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

Jean Bertoin (2008). Two-parameter Poisson-Dirichlet measures and reversible
exchangeable fragmentation-coalescence processes. Combin. Probab. Comp. 17, 329 - 337, 2008

Jean Bertoin, Ron Doney, Ross Maller (2008). Passage of Lévy processes across power law boundaries at small times. Ann. Probab. 36, 160 - 197, 2008

Jean Bertoin (2007). Reflecting a Langevin process at an absorbing boundary. Ann. Probab. 35, 2021 - 2037, 2007

Jean Bertoin, Takao Fujita, Bernard Roynette, Marc 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

Jean Bertoin, Jean-François Le Gall (2006). Stochastic flows associated to coalescent processes III: Limits theorems. Illinois J. Math. 50, 147 - 181, 2006

Jean Bertoin, Grégory Miermont (2006). Asymptotics in Knuth's parking problem for caravans. Random Structures Algorithms 29, 38 - 55, 2006

Jean Bertoin (2006). Some aspects of a random fragmentation model. Stochastic Process. Appl. 116, 345 - 369, 2006

Jean Bertoin, Marc Yor (2005). Exponential functionals of Lévy processes. Probability Survey 2, 191 - 212, 2005

Jean Bertoin. SLE et invariance conforme (d'après Lawler, Schramm et Werner). Séminaire Bourbaki, Volume 2003/2004
Astérisque 299, 15 - 28, 2005

Jean Bertoin, Jean-François Le Gall (2005). Stochastic flows associated to coalescent processes II:
Stochastic differential equation. Ann. Inst. Henri Poincaré 41, 307 - 333, 2005

Jean Bertoin, Servet Martinez (2005). Fragmentation energy. Adv. Appl. Probab. 37, 553 - 570, 2005

Jean Bertoin, Alain Rouault (2005). Discretization methods for homogeneous fragmentations. J. London Math. Soc. 72, 91 - 109, 2005

Jean Bertoin, Philippe Biane, Marc 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

Jean Bertoin, Christina 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

Jean Bertoin, A. V. Gnedin (2004). Asymptotic laws for nonconservative self-similar fragmentations. Electron. J. Probab. 9, 575 - 593, 2004

Jean Bertoin (2004). Random covering of an interval and a variation of Kingman's coalescent. Random Structures Algorithms 25, 277 -292, 2004

Jean 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

Jean Bertoin (2004). On small masses in self-similar fragmentations. Stochastic Process. Appl. 109, 13 - 22, 2004

Jean Bertoin, Loic Chaumont, Jim Pitman (2003). Path transformations of first passage bridges. Electron. Commun. Probab. 8, 155 - 166, 2003

Jean Bertoin (2003). The asymptotic behavior of fragmentation processes. J. Euro. Math. Soc 5, 395 - 416, 2003

Jean Bertoin, Jean-François Le Gall (2003). Stochastic flows associated to coalescent processes. Probab. Theory Relat. Fields 126, 261 - 288, 2003

Jean Bertoin, Marc 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

Jean Bertoin (2002). Self-attracting Poisson clouds in an expanding universe. Commun. Math. Phys. 232, 59 - 81, 2002

Jean Bertoin (2002). Some aspects of additive coalescents. Proceedings ICM 2002 vol. III, Higher Education Press, 15 - 23, 2002

Jean Bertoin (2002). Eternal solutions to Smoluchowski's coagulation equation with additive kernel
and their probabilistic interpretations. Ann. Appl. Probab. 12, 547 - 564, 2002

Jean Bertoin, Marc Yor (2002). Entrance laws of self-similar Markov processes and
exponential functionals of Lévy processes. Potential Analysis 17, 389 - 400, 2002

Jean Bertoin, Maria-Emilia Caballero (2002). Entrance from 0+ for increasing semi-stable Markov processes. Bernoulli 8, 195 - 205, 2002

Jean Bertoin (2002). Self-similar fragmentations. Ann. Inst. Henri Poincaré 38, 319 - 340, 2002

Jean Bertoin, Marc Yor (2001). On subordinators, self-similar Markov processes, and some factorizations
of the exponential law. Electron. Commun. in Probab. 6, 95 - 106, 2001

Jean Bertoin, Christophe Giraud, Yukio Isozaki (2001). Statistics of a flux in Burgers turbulence with one-sided Brownian initial data. Commun. Math. Phys. 224, 551 - 564, 2001

Jean Bertoin (2001). Homogeneous fragmentation processes. Probab. Theory Relat. Fields 121, 301 -318, 2001

Jean Bertoin (2001). Eternal additive coalescents and certain bridges with exchangeable increments. Ann. Probab. 29, 344 - 360, 2001

Jean 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

Jean Bertoin (2001). Elements on Lévy processes. Stochastic Processes: Theory and Methods
Handbook of Statistics 19, Elsevier, 117 - 144, 2001

Jean Bertoin (2000). A fragmentation process connected to Brownian motion. Probab. Theory Relat. Fields 117, 289 - 301, 2000

Jean Bertoin, Jean-François Le Gall (2000). The Bolthausen-Sznitman coalescent and the genealogy of
continuous-state branching processes. Probab. Theory Relat. Fields 117, 249 - 266, 2000

Jean Bertoin, Jim Pitman (2000). Two coalescents derived from the range of stable subordinators. Electron. J. Probab. 5, 1 - 17, 2000

Jean Bertoin (2000). The convex minorant of the Cauchy process. Electron. Commun. in Probab. 5, 51 - 55, 2000

Jean Bertoin (2000). Clustering statistics for sticky particles with Brownian initial velocity. J. Math. Pures Appl. 79, 173 - 194, 2000

Jean Bertoin (1999). renewal theory for embedded regenerative sets. Ann. Probab. 27, 1523 - 1535, 1999

Jean Bertoin (1999). Subordinators: Examples and Applications. Ecole d'été de Probabilités de St-Flour XXVII
Lect. Notes in Maths 1717, Springer, 1 - 91, 1999

Jean Bertoin, Klaas van Harn, F.W. Steutel (1999). Renewal theory and level passage by subordinators. Stat. Probab. Letters 45, 65 - 69, 1999

Jean Bertoin (1999). On overshoots and hitting times for random walks. J. Appl. Probab. 36, 593 - 600, 1999

Jean Bertoin, Jim Pitman, Jose Ruiz de Chavez (1999). Construction of a Brownian path with a given minimum. Electron. Commun. in Probab. 4, 31 - 37, 1999

Jean Bertoin (1999). Structure of shocks in Burgers turbulence with stable noise initial data. Commun. Math. Phys. 203, 729 - 741, 1999

Jean Bertoin (1999). Intersection of independent regenerative sets. Probab. Theory Relat. Fields 114, 97 - 121, 1999

Jean Bertoin, Maria-Emilia Caballero (1999). Regularity of the Cauchy principal value of the local times of some Lévy processes. Bull. Sc. math. 123, 47 - 58, 1999