Quentin Berger

Research interests:


I work in the field of Probability and statistical physics, and I study in particular disordered systems. I am particularly interested in polymer models, among other topics.
Keywords: Statistical physics, disordered systems, stochastic PDEs, random polymers, phase transition, critical phenomena, influence of disorder, random walks, renewal processes, random graphs, first-passage percolation, last-passage percolation...

Publications and preprints:

Here is a list of my collaborators (by alphabetical order):
Kenneth S. Alexander, Irene Ayuso Ventura, Loïc Béthencourt, Matthias Birkner, Céline Bonnet, Nicolas Bouchot, Francesco Caravenna, Carsten Chong, Frank den Hollander, Giambattista Giacomin, Chien-Hao Huang, Maha Khatib, Hubert Lacoin, Lucile Laulin, Alexandre Legrand, Brune Massoulié, Julien Poisat, Rémy Poudevigne-Auboiron, Kilian Raschel, Christophe Sabot, Michele Salvi, Rongfeng Sun, Camille Tardif, Fabio L. Toninelli, Niccolò Torri, Nicola Turchi, Ran Wei, Linglong Yuan, Nikos Zygouras.
My publications are listed below, classified by topic (and by anti-chronological order below).
All preprint versions are available on arXiv or HAL.
  1. Quentin Berger, Francesco Caravenna, Nicola Turchi,
    Strong disorder for Stochastic Heat Flow and 2D Directed Polymers,
    arXiv:2508.02478 [math.PR]
  2. Quentin Berger, Carsten Chong, Hubert Lacoin,
    The Stochastic Heat Equation with multiplicative Lévy noise: Existence, moments, and intermittency,
    Commun. Math. Phys., Vol. 402 (2023), pp. 2215–2299.
    [Journal] [arXiv]
  3. Quentin Berger, Hubert Lacoin,
    The continuum directed polymer in Lévy Noise,
    J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
    [Journal] [arXiv]
  1. Quentin Berger, Alexandre Legrand, Rémy Poudevigne-Auboiron, Christophe Sabot,
    A random polymer approach to the weak disorder phase of the vertex reinforced jump process,
    arXiv:2503.10209 [math.PR]
  2. Quentin Berger, Chien-Hao Huang, Niccoló Torri, Ran Wei,
    One-dimensional polymers in random environments: stretching vs. folding,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-45.
    [Journal] [arXiv]
  3. Quentin Berger, Niccoló Torri, Ran Wei,
    Non-directed polymers in heavy-tail random environment in dimension d≥2,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-67.
    [Journal] [arXiv]
  4. Quentin Berger, Hubert Lacoin,
    The scaling limit of the directed polymer with power-law tail disorder,
    Commun. Math. Phys., Vol. 386 (2021), pp. 1051-1105.
    [Journal] [arXiv]
  5. Quentin Berger, Niccoló Torri,
    Directed polymers in heavy-tail random environment,
    Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
    [Journal] [arXiv]
  6. Quentin Berger, Hubert Lacoin,
    The high-temperature behavior for the directed polymer in dimension 1+2,
    Ann. Inst. Henri Poincaré: Probab. Stat., Vol. 53 (2017), no 1, 430–450.
    [Journal] [arXiv]
  1. Quentin Berger, Hubert Lacoin,
    The Random Walk Pinning Model I: Lower bounds on the free energy and disorder irrelevance,
    arXiv:2509.08789 [math.PR]
  2. Quentin Berger, Hubert Lacoin,
    The Random Walk Pinning Model II: Upper bounds on the free energy and disorder relevance,
    arXiv:2509.08769 [math.PR]
  3. Quentin Berger, Brune Massoulié,
    Wetting on a wall and wetting in a well: Overview of equilibrium properties,
    Stochastic Process. Appl., Vol. 170 (2024), Special issue in tribute to Francis Comets.
    [Journal] [arXiv]
  4. Quentin Berger, Giambattista Giacomin, Hubert Lacoin,
    Disorder and critical phenomena: the α=0 copolymer model,
    Probab. Theory Relat. Fields, Vol. 174, Issue 3-4 (2019), pp. 787–819.
    [Journal] [arXiv]
  5. Kenneth S. Alexander, Quentin Berger,
    Pinning of a renewal on a quenched renewal,
    Electron. J. Probab., Vol. 23 (2018), no 6, 48 pp.
    [Journal] [arXiv]
  6. Quentin Berger, Hubert Lacoin,
    Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift,
    J. Inst. Math. Jussieu, Vol. 17 (2018), Issue 2, 305-346.
    [Journal] [arXiv]
  7. Quentin Berger, Julien Poisat,
    On the critical curve of the pinning and copolymer models in correlated Gaussian environment,
    Electron. J. Probab., Vol. 20 (2015), no 71, 1-35.
    [Journal] [arXiv]
  8. Quentin Berger,
    Pinning model in random correlated environment: appearance of an infinite disorder regime,
    J. Stat. Phys., Vol. 155, Issue 3 (2014), 544-570.
    [Journal] [arXiv]
  9. Quentin Berger, Francesco Caravenna, Julien Poisat, Rongfeng Sun, Nikos Zygouras,
    The critical curve of the random pinning and copolymer models at weak coupling,
    Comm. Math. Phys., Vol 326, Issue 2 (2014) 507-530.
    [Journal] [arXiv]
  10. Quentin Berger,
    Comments on the influence of disorder for pinning model in Gaussian correlated environment,
    ALEA, Lat. Am. J. Probab. Math. Stat. X (2), (2013) 953–977.
    [Journal] [arXiv]
  11. Quentin Berger, Fabio Toninelli,
    Hierachical pinning model in correlated random environment,
    Ann. Inst. Henri Poincaré Probab. Stat., Vol. 48 Num. 3 (2013) 781-816.
    [Journal] [arXiv]
  12. Quentin Berger, Hubert Lacoin,
    Sharp critical behavior for random pinning model with correlated environment,
    Stochastic Process. Appl., Vol. 122, Issue 4 (2012) 1397-1436.
    [Journal] [arXiv]
  13. Quentin Berger, Hubert Lacoin,
    The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics,
    J. Stat. Phys., Vol. 142, Issue 2 (2011) 322-341.
    [Journal] [arXiv]
  14. Quentin Berger, Fabio Toninelli,
    On the critical point of the Random Walk Pinning Model in dimension d=3,
    Electron. J. Probab. Vol. 15 (2010) no 21, 654-683.
    [Journal] [arXiv]
  1. Quentin Berger, Alexandre Legrand,
    Scaling limit of the disordered generalized Poland-Scheraga model for DNA denaturation
    Probab. Theory Relat. Fields, Vol. 190 (2024) pp. 179–258.
    [Journal] [arXiv]
  2. Quentin Berger, Giambattista Giacomin, Maha Khatib,
    Disorder and denaturation transition in the generalized Poland-Scheraga model,
    Ann. Henri Lebesgue, Vol. 3 (2020), pp. 299-339.
    [Journal] [arXiv]
  3. Quentin Berger, Giambattista Giacomin, Maha Khatib,
    DNA melting structures in the generalized Poland-Scheraga model,
    ALEA, Lat. Am. J. Probab. Math. Stat., Vol. 15 (2018), pp 993-1025.
    [Journal] [arXiv]
  4. Quentin Berger, Frank den Hollander, Julien Poisat,
    Annealed scaling for a charged polymer in dimensions two and higher,
    J. Phys. A: Math. Theor, Vol. 51, no 5 (2018), special issue in honour of Stuart Whittington’s 75th birthday.
    [Journal] [arXiv]
  1. Quentin Berger, Nicolas Bouchot,
    Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings,
    arXiv:2408.15858v2 [math.PR]
  2. Quentin Berger, Loïc Béthencourt, Camille Tardif,
    On joint returns to zero of Bessel processes,
    arXiv:2406.19344 [math.PR]
  3. Quentin Berger, Loïc Béthencourt, Camille Tardif,
    Persistence problems for additive functionals of one-dimensional Markov processes ,
    to appear in Ann. Inst. Henri Poincaré: Probab. Stat.,
    arXiv:2304.09034 [math.PR]
  4. Quentin Berger, Loïc Béthencourt,
    An application of Sparre Andersen's fluctuation theorem for exchangeable and sign-invariant random variables,
    Séminaire de Probabilités LII (2025), Chapter 9, pp. 367--388
    [Journal] [arXiv]
  5. Quentin Berger, Matthias Birkner, Linglong Yuan,
    Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon,
    Ann. Fac. Sci. Toulouse: Math., Série 6, Tome 33 (2024) no. 5, pp. 1413-1485.
    [Journal] [arXiv]
  6. Quentin Berger,
    Notes on Random Walks in the Cauchy domain of attraction,
    Probab. Theory Relat. Fields, Vol. 175, Issue 1-2 (2019), pp. 1-44.
    [Journal] [arXiv]
  7. Quentin Berger,
    Strong renewal theorems and local large deviations for multivariate random walks and renewals,
    Electron. J. Probab., Vol. 24, no. 46 (2019), 47 pp.
    [Journal] [arXiv]
  8. Kenneth S. Alexander, Quentin Berger,
    Local asymptotics for the first intersection of two independent renewals,
    Electron. J. Probab., Vol. 21 (2016), no 68, 1-20.
    [Journal] [arXiv]
  9. Kenneth S. Alexander, Quentin Berger,
    Local limit theorem and renewal theory with no moments,
    Electron. J. Probab., Vol. 21 (2016), no 66, 1-18.
    [Journal] [arXiv]
  1. Quentin Berger, Niccoló Torri,
    Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints,
    Ann. Inst. Henri Poincaré: Comb., Phys. Inter., Vol. 8, Num. 2 (2021), pp. 213-241.
    [Journal] [arXiv]
  2. Quentin Berger, Niccoló Torri,
    Entropy-controlled Last-Passage Percolation,
    Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
    [Journal] [arXiv]
  3. Kenneth S. Alexander, Quentin Berger,
    Geodesics Toward Corners in First Passage Percolation,
    J. Stat. Phys., Vol. 172, Issue 4 (2018), pp 1029-1056.
    [Journal] [arXiv]
  1. Quentin Berger, Michele Salvi,
    Scaling limit of sub-ballistic 1D Random Walk among biased conductances: a story of wells and walls,
    Electron. J. Probab., Vol. 25, no 30 (2020), 43 pp.
    [Journal] [arXiv]
  2. Quentin Berger, Michele Salvi,
    Scaling of sub-ballistic 1D Random Walks among biased Random Conductances,
    Markov Processes Relat. Fields, Vol. 25, Issue 1 (2019), pp 171-187.
    [Journal] [arXiv]
  1. Irene Ayuso Ventura, Quentin Berger,
    Non-linear conductances of Galton-Watson trees and application to the (near) critical random cluster model,
    arXiv:2404.11564 [math.PR]
  2. Irene Ayuso Ventura, Quentin Berger,
    Ising model on a Galton-Watson tree with a sparse random external field,
    Electron. J. Probab., Vol. 29, no 174 (2024) 43pp.
    [Journal] [arXiv]

Ph.D. Thesis

I did my Ph.D. under the supervision of Fabio Toninelli, at École Normale Supérieure de Lyon (France).
Title: Polymères en milieu aléatoire: influence d'un désordre corrélé sur le phénomène de localisation, (partially in French). Link.

Habilitation

Here is the manuscript of my Habilitation à diriger des recherches:
Random polymers and related models: disorder, localization and critical phenomena.

Proceedings

  • Quentin Berger, Céline Bonnet, Lucile Laulin, Kilian Raschel,
    Topics in random walks,
    ESAIM: Proceedings and Surveys, Vol. 80, p. 51 (2025), Modélisation aléatoire et stochastique - Journées MAS 2022.
    [Journal] [PDF]
  • Quentin Berger,
    Influence of disorder for polymer pinning models,
    ESAIM: Proceedings and Surveys, Vol. 51, p. 74 (2015), Modélisation aléatoire et stochastique - Journées MAS 2014.
    [Journal] [PDF]

Large audience articles

Articles by anti-chronological order

    Preprints

  1. Quentin Berger, Hubert Lacoin,
    The Random Walk Pinning Model I: Lower bounds on the free energy and disorder irrelevance,
    arXiv:2509.08789 [math.PR]
  2. Quentin Berger, Hubert Lacoin,
    The Random Walk Pinning Model II: Upper bounds on the free energy and disorder relevance,
    arXiv:2509.08769 [math.PR]
  3. Quentin Berger, Francesco Caravenna, Nicola Turchi,
    Strong disorder for Stochastic Heat Flow and 2D Directed Polymers,
    arXiv:2508.02478 [math.PR]
  4. Quentin Berger, Alexandre Legrand, Rémy Poudevigne-Auboiron, Christophe Sabot,
    A random polymer approach to the weak disorder phase of the vertex reinforced jump process,
    arXiv:2503.10209 [math.PR]
  5. Quentin Berger, Nicolas Bouchot,
    Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings,
    arXiv:2408.15858v2 [math.PR]
  6. Quentin Berger, Loïc Béthencourt, Camille Tardif,
    On joint returns to zero of Bessel processes,
    arXiv:2406.19344 [math.PR]
  7. Irene Ayuso Ventura, Quentin Berger,
    Non-linear conductances of Galton-Watson trees and application to the (near) critical random cluster model,
    arXiv:2404.11564 [math.PR]

    8. To appear

  8. Quentin Berger, Loïc Béthencourt, Camille Tardif,
    Persistence problems for additive functionals of one-dimensional Markov processes,
    to appear in Ann. Inst. Henri Poincaré: Probab. Stat.,
    arXiv:2304.09034 [math.PR]

    9. 2025

  9. Quentin Berger, Loïc Béthencourt,
    An application of Sparre Andersen's fluctuation theorem for exchangeable and sign-invariant random variables,
    Séminaire de Probabilités LII (2025), Chapter 9, pp. 367--388
    [Journal] [arXiv]
  10. Quentin Berger, Céline Bonnet, Lucile Laulin, Kilian Raschel,
    Topics in random walks,
    ESAIM: Proceedings and Surveys, Vol. 80, p. 51 (2025), Modélisation aléatoire et stochastique - Journées MAS 2022.
    [Journal] [PDF]

    11. 2024

  11. Quentin Berger, Matthias Birkner, Linglong Yuan,
    Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon,
    Ann. Fac. Sci. Toulouse: Math., Série 6, Tome 33 (2024) no. 5, pp. 1413-1485.
    [Journal] [arXiv]
  12. Irene Ayuso Ventura, Quentin Berger,
    Ising model on a Galton-Watson tree with a sparse random external field,
    Electron. J. Probab., Vol. 29, no 174 (2024) 43pp.
    [Journal] [arXiv]
  13. Quentin Berger, Alexandre Legrand,
    Scaling limit of the disordered generalized Poland-Scheraga model for DNA denaturation
    Probab. Theory Relat. Fields, Vol. 190 (2024) pp. 179–258.
    [Journal] [arXiv]
  14. Quentin Berger, Brune Massoulié,
    Wetting on a wall and wetting in a well: Overview of equilibrium properties,
    Stochastic Process. Appl., Vol. 170 (2024), Special issue in tribute to Francis Comets.
    [Journal] [arXiv]

    15. 2023

  15. Quentin Berger, Carsten Chong, Hubert Lacoin,
    The Stochastic Heat Equation with multiplicative Lévy noise: Existence, moments, and intermittency,
    Commun. Math. Phys., Vol. 402 (2023), pp. 2215–2299.
    [Journal] [arXiv]

    16. 2022

  16. Quentin Berger, Chien-Hao Huang, Niccoló Torri, Ran Wei,
    One-dimensional polymers in random environments: stretching vs. folding,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-45.
    [Journal] [arXiv]
  17. Quentin Berger, Hubert Lacoin,
    The continuum directed polymer in Lévy Noise,
    J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
    [Journal] [arXiv]
  18. Quentin Berger, Niccoló Torri, Ran Wei,
    Non-directed polymers in heavy-tail random environment in dimension d≥2,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-67.
    [Journal] [arXiv]

    19. 2021

  19. Quentin Berger, Hubert Lacoin,
    The scaling limit of the directed polymer with power-law tail disorder,
    Commun. Math. Phys., Vol. 386 (2021), pp. 1051-1105.
    [Journal] [arXiv]
  20. Quentin Berger, Niccoló Torri,
    Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints,
    Ann. Inst. Henri Poincaré: Comb., Phys. Inter., Vol. 8, Num. 2 (2021), pp. 213-241.
    [Journal] [arXiv]

    21. 2020

  21. Quentin Berger, Giambattista Giacomin, Maha Khatib,
    Disorder and denaturation transition in the generalized Poland-Scheraga model,
    Ann. Henri Lebesgue, Vol. 3 (2020), pp. 299-339.
    [Journal] [arXiv]
  22. Quentin Berger, Michele Salvi,
    Scaling limit of sub-ballistic 1D Random Walk among biased conductances: a story of wells and walls,
    Electron. J. Probab., Vol. 25, no 30 (2020), 43 pp.
    [Journal] [arXiv]

    23. 2019

  23. Quentin Berger,
    Notes on Random Walks in the Cauchy domain of attraction,
    Probab. Theory Relat. Fields, Vol. 175, Issue 1-2 (2019), pp. 1-44.
    [Journal] [arXiv]
  24. Quentin Berger,
    Strong renewal theorems and local large deviations for multivariate random walks and renewals,
    Electron. J. Probab., Vol. 24, no. 46 (2019), 47 pp.
    [Journal] [arXiv]
  25. Quentin Berger, Giambattista Giacomin, Hubert Lacoin,
    Disorder and critical phenomena: the α=0 copolymer model,
    Probab. Theory Relat. Fields, Vol. 174, Issue 3-4 (2019), pp. 787–819.
    [Journal] [arXiv]
  26. Quentin Berger, Michele Salvi,
    Scaling of sub-ballistic 1D Random Walks among biased Random Conductances,
    Markov Processes Relat. Fields, Vol. 25, Issue 1 (2019), pp 171-187.
    [Journal] [arXiv]
  27. Quentin Berger, Niccoló Torri,
    Directed polymers in heavy-tail random environment,
    Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
    [Journal] [arXiv]
  28. Quentin Berger, Niccoló Torri,
    Entropy-controlled Last-Passage Percolation,
    Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
    [Journal] [arXiv]

    29. 2018

  29. Kenneth S. Alexander, Quentin Berger,
    Geodesics Toward Corners in First Passage Percolation,
    J. Stat. Phys., Vol. 172, Issue 4 (2018), pp 1029-1056.
    [Journal] [arXiv]
  30. Kenneth S. Alexander, Quentin Berger,
    Pinning of a renewal on a quenched renewal,
    Electron. J. Probab., Vol. 23 (2018), no 6, 48 pp.
    [Journal] [arXiv]
  31. Quentin Berger, Giambattista Giacomin, Maha Khatib,
    DNA melting structures in the generalized Poland-Scheraga model,
    ALEA, Lat. Am. J. Probab. Math. Stat., Vol. 15 (2018), pp 993-1025.
    [Journal] [arXiv]
  32. Quentin Berger, Frank den Hollander, Julien Poisat,
    Annealed scaling for a charged polymer in dimensions two and higher,
    J. Phys. A: Math. Theor, Vol. 51, no 5 (2018), special issue in honour of Stuart Whittington’s 75th birthday.
    [Journal] [arXiv]
  33. Quentin Berger, Hubert Lacoin,
    Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift,
    J. Inst. Math. Jussieu, Vol. 17 (2018), Issue 2, 305-346.
    [Journal] [arXiv]

    34. 2017

  34. Quentin Berger, Hubert Lacoin,
    The high-temperature behavior for the directed polymer in dimension 1+2,
    Ann. Inst. Henri Poincaré: Probab. Stat., Vol. 53 (2017), no 1, 430–450.
    [Journal] [arXiv]

    35. 2016

  35. Kenneth S. Alexander, Quentin Berger,
    Local asymptotics for the first intersection of two independent renewals,
    Electron. J. Probab., Vol. 21 (2016), no 68, 1-20.
    [Journal] [arXiv]
  36. Kenneth S. Alexander, Quentin Berger,
    Local limit theorem and renewal theory with no moments,
    Electron. J. Probab., Vol. 21 (2016), no 66, 1-18.
    [Journal] [arXiv]

    37. 2010–2015

  37. Quentin Berger, Julien Poisat,
    On the critical curve of the pinning and copolymer models in correlated Gaussian environment,
    Electron. J. Probab., Vol. 20 (2015), no 71, 1-35.
    [Journal] [arXiv]
  38. Quentin Berger,
    Influence of disorder for polymer pinning models,
    ESAIM: Proceedings and Surveys Vol. 51, p.74 (October 2015), Modélisation aléatoire et stochastique - Journées MAS 2014.
    [Journal] [PDF]
  39. Quentin Berger,
    Pinning model in random correlated environment: appearance of an infinite disorder regime,
    J. Stat. Phys., Vol. 155, Issue 3 (2014), 544-570.
    [Journal] [arXiv]
  40. Quentin Berger, Francesco Caravenna, Julien Poisat, Rongfeng Sun, Nikos Zygouras,
    The critical curve of the random pinning and copolymer models at weak coupling,
    Comm. Math. Phys., Vol 326, Issue 2 (2014) 507-530.
    [Journal] [arXiv]
  41. Quentin Berger,
    Comments on the influence of disorder for pinning model in Gaussian correlated environment,
    ALEA, Lat. Am. J. Probab. Math. Stat. X (2), (2013) 953–977.
    [Journal] [arXiv]
  42. Quentin Berger, Fabio Toninelli,
    Hierachical pinning model in correlated random environment,
    Ann. Inst. Henri Poincaré Probab. Stat., Vol. 48 Num. 3 (2013) 781-816.
    [Journal] [arXiv]
  43. Quentin Berger, Hubert Lacoin,
    Sharp critical behavior for random pinning model with correlated environment,
    Stochastic Process. Appl., Vol. 122, Issue 4 (2012) 1397-1436.
    [Journal] [arXiv]
  44. Quentin Berger, Hubert Lacoin,
    The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics,
    J. Stat. Phys., Vol. 142, Issue 2 (2011) 322-341.
    [Journal] [arXiv]
  45. Quentin Berger, Fabio Toninelli,
    On the critical point of the Random Walk Pinning Model in dimension d=3,
    Electron. J. Probab. Vol. 15 (2010) no 21, 654-683.
    [Journal] [arXiv]