Publications and prepublications list

I'm mainly interested in branching processes, in particular branching random walks and branching Lévy process. Below is my list of preprints and publications in mathematics journals, organised by date. Also available are popularisation articles, my school productions as well as unpublished notes. Feel free to contact me if you have any quesitons about my articles, or if you notice any mistake in the dedicated pages.

Preprints

• Freezing in the Infinite-Bin Model
  Bastien Mallein, Sanjay Ramassamy and Arvind Singh [pdf, arXiv, hal, bib]
• Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
  Sergey Foss, Takis Konstantopoulos, Bastien Mallein and Sanjay Ramassamy [pdf, arXiv, bib]
• Fragmentation processes and the convex hull of the Brownian motion in a disk
  Bénédicte Haas and Bastien Mallein [pdf, arXiv, bib]
• Reinforced Galton-Watson processes II: Large time behaviors
  Jean Bertoin and Bastien Mallein [pdf, arXiv, bib]
• KPP traveling waves in the half-space
  Julien Berestycki, Cole Graham, Yujin H. Kim and Bastien Mallein [pdf, arXiv, bib]
• Tight estimates of exit and containment probabilities for nonlinear stochastic systems
  Quang-Cuong Pham, Bastien Mallein and Jean-Jacques Slotine [pdf, arXiv, hal, bib]

Publications

• Reinforced Galton-Watson processes I: Malthusian exponents
  Jean Bertoin and Bastien Mallein Random Structures Algorithms (2024), 1--24. [pdf, arXiv, hal, bib]
• The extremal point process of branching Brownian motion in ℝ^d
  Julien Berestycki, Yujin H. Kim, Eyal Lubetzky, Bastien Mallein and Ofer Zeitouni Ann. Probab. 52 (2024), no. 3, 955-982. [pdf, arXiv, hal, bib]
• Branching Brownian motion conditioned on small maximum
  Xinxin Chen, Hui He and Bastien Mallein ALEA, Lat. Am. J. Probab. Math. Stat. 20 (2023), no. 2, 905--940. [pdf, arXiv, hal, bib]
• Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
  Sergey Foss, Takis Konstantopoulos, Bastien Mallein and Sanjay Ramassamy ALEA, Lat. Am. J. Probab. Math. Stat. 20 (2023), no. 1, 547--560. [pdf, arXiv, hal, bib]
• A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process
  Bastien Mallein and Quan Shi Bernoulli 29 (2023), no. 1, 597--624. [pdf, arXiv, hal, bib]
• A simple backward construction of Branching Brownian motion with large displacement and applications
  Julien Berestycki, Éric Brunet, Aser Cortines and Bastien Mallein Ann. Inst. Henri Poincaré, Probab. Stat. 58 (2022), no. 4, 2094--2113. [pdf, arXiv, hal, bib]
• On the length of the shortest path in a sparse Barak-Erdős graph
  Bastien Mallein and Pavel Tesemnikov Stat. Probab. Lett. 190 (2022), 5 p.. [pdf, arXiv, hal, bib]
• A tractable non-adaptative group testing method for non-binary measurements
  Emilien Joly and Bastien Mallein ESAIM Probab. Stat. 26 (2022), 283--303. [pdf, arXiv, hal, bib]
• Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case
  Xinxin Chen and Bastien Mallein Electron. Commun. Probab. 27 (2022), no. 7, 11 pp. [pdf, arXiv, hal, bib]
• A simple method to find all solutions to the functional equation of the smoothing transform
  Gerold Alsmeyer and Bastien Mallein J. Theor. Probab. (2022), 31 pp. [pdf, arXiv, hal, bib]
• Late levels of nested occupancy scheme in random environment
  Alexander Iksanov and Bastien Mallein Stochastic Models 38 (2022), no. 1, 130--166. [pdf, arXiv, hal, bib]
• On the branching convolution equation E=Z⊛E
  Pascal Maillard and Bastien Mallein Electron. Commun. Probab. 26 (2021), no. 59, 12 pp. [pdf, arXiv, hal, bib]
• Anomalous spreading in reducible multitype branching Brownian motion
  Mohamed Ali Belloum and Bastien Mallein Electron. J. Probab. 26 (2021), no. 61, 39 pp. [pdf, arXiv, hal, bib]
• Group testing as a strategy for the epidemiologic monitoring of COVID-19
  Vincent Brault, Bastien Mallein and Jean-François Rupprecht PLOS Comput. Biol. 17 (2021), no. 3, 25 pp. [pdf, arXiv, hal, bib]
• Barak-Erdős graphs and the infinite-bin model
  Bastien Mallein and Sanjay Ramassamy Ann. Instit. Henri Poincaré Probab. Stat. 57 (2021), no. 4, 1940--1967. [pdf, arXiv, hal, bib]
• Derivative martingale of the branching Brownian motion in dimension d≥1
  Roman Stasiński, Julien Berestycki and Bastien Mallein Ann. Instit. Henri Poincaré Probab. Stat. 57 (2021), no. 3, 1786--1810. [pdf, arXiv, hal, bib]
• On the derivative martingale in a branching random walk
  Dariusz Buraczewski, Alexander Iksanov and Bastien Mallein Ann. Probab. 49 (2021), no. 3, 1164--1204. [pdf, arXiv, hal, bib]
• An exactly solvable continuous-time Derrida--Retaux model
  Yueyun Hu, Bastien Mallein and Michel Pain Comm. Math. Phys. 375 (2020), no. 1, 605--651. [pdf, arXiv, hal, bib]
• Coalescences in Continuous-State Branching Processes
  Clément Foucart, Chunhua Ma and Bastien Mallein Electron. J. Probab. 24 (2019), no. 103, 52 pp. [pdf, arXiv, hal, bib]
• Capturability-based Pattern Generation for Walking with Variable Height
  Stéphane Caron, Adrien Escande, Leonardo Lanari and Bastien Mallein IEEE T-RO 36 (2020), no. 2, 517--536. [pdf, arXiv, hal, bib]
• A result on power moments of Lévy-type perpetuities and its application to the Lp-convergence of Biggins' martingales in branching Lévy processes.
  Alexander Iksanov and Bastien Mallein ALEA Lat. Am. J. Prob. Math. Stat. 16 (2019), no. 1, 315--331. [pdf, arXiv, hal, bib]
• Two-sided infinite-bin models and analyticity for Barak–Erdős graphs
  Bastien Mallein and Sanjay Ramassamy Bernoulli 25 (2019), no. 4B, 3479 -- 3495. [pdf, arXiv, hal, bib]
• On the trajectory of an individual chosen according to supercritical Gibbs measure in the branching random walk
  Xinxin Chen, Thomas Madaule and Bastien Mallein Stochastic Process. Appl. 129 (2019), no. 10, 3821--3858. [pdf, arXiv, hal, bib]
• Infinitely ramified point measures and branching Lévy processes
  Jean Bertoin and Bastien Mallein Ann. Probab. 47 (2019), no. 3, 1619--1652. [pdf, arXiv, hal, bib]
• Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment
  Bastien Mallein and Piotr Miłoś Stochastic Process. Appl. 129 (2019), no. 9, 3239--3260. [pdf, arXiv, hal, bib]
• Necessary and sufficient conditions for the convergence of the consistent maximal displacement of the branching random walk
  Bastien Mallein Braz. J. Probab. Stat. 33 (2019), no. 2, 356--373. [pdf, arXiv, hal, bib]
• The genealogy of an exactly solvable Ornstein-Uhlenbeck type branching process with selection
  Aser Cortines and Bastien Mallein Electron. Commun. Probab. 23 (2018), no. 98, 13 pp. [pdf, arXiv, hal, bib]
• Branching-stable point processes and measures
  Jean Bertoin, Aser Cortines and Bastien Mallein Adv. Appl. Probab. 50 (2018), no. 4, 1294--1314. [pdf, arXiv, hal, bib]
• Biggins' Martingale Convergence for Branching Lévy Processes
  Jean Bertoin and Bastien Mallein Electron. Commun. Probab. 23 (2018), no. 83, 12 pp. [pdf, arXiv, hal, bib]
• Brownian Motion and Random Walk above Quenched Random Wall
  Bastien Mallein and Piotr Miłoś Ann. Instit. Henri Poincaré Probab. Stat. 54 (2018), no. 4, 1877--1916. [pdf, arXiv, hal, bib]
• Genealogy of the extremal process of the branching random walk
  Bastien Mallein ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 2, 1065--1087. [pdf, arXiv, hal, bib]
• Balance Control Using Both ZMP and COM Height Variations: A Convex Boundedness Approach
  Stéphane Caron and Bastien Mallein ICRA 2018 (2018), 1779--1784. [pdf, arXiv, hal, bib]
• Branching random walks with trapping zones
  Romain Biard, Bastien Mallein and Landy Rabehasaina Stochastic Process. Appl. 128 (2018), no. 7, 2341--2366. [pdf, arXiv, hal, bib]
• N-branching random walk with α-stable spine
  Bastien Mallein Theor. Probab. Appl. 62 (2018), no. 2, 295--318. [pdf, arXiv, hal, bib]
• Second order behavior of the block counting process of beta coalescents
  Yier Lin and Bastien Mallein Electron. Commun. Probab. 22 (2017), no. 61, 8 pp. [pdf, arXiv, hal, bib]
• Branching random walk with selection at critical rate
  Bastien Mallein Bernoulli 23 (2017), no. 3, 1784--1821. [pdf, arXiv, hal, bib]
• A N-branching random walk with random selection
  Aser Cortines and Bastien Mallein ALEA Lat. Am. J. Probab. Math. Stat. 14 (2017), no. 1, 117--137. [pdf, arXiv, hal, bib]
• Maximal displacement of d-dimensional branching Brownian motion
  Bastien Mallein Electron. Commun. Probab. 20 (2015), no. 76, 12 pp. [pdf, arXiv, hal, bib]
• Maximal displacement of a branching random walk in time-inhomogeneous environment
  Bastien Mallein Stochastic Process. Appl. 125 (2015), no. 10, 3958--4019. [pdf, arXiv, hal, bib]
• Maximal displacement in a branching random walk through interfaces
  Bastien Mallein Electron. J. Probab. 20 (2015), no. 68, 40 pp. [pdf, arXiv, hal, bib]

Scientific popularisation

• Asymptotic of the maximal displacement in a branching random walk.
  Bastien Mallein, Graduate J. Math., 1 (2016), no. 2, 92--104. [pdf, arXiv, hal, bib]

Unpublished notes

• A short proof of the asymptotic of the minimum of the branching random walk after time n [pdf, arXiv, bib].

Student's theses

• PhD thesis : Branching random walks, time-inhomogeneous environment, selection, under direction of Zhan Shi.
• Master thesis : Convergence of certain classes of superprocesses toward Dawson-Watanabe superprocesses, under direction of Edwin Perkins.