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, 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, Nicolas Bouchot, Francesco Caravenna, Carsten Chong, Frank den Hollander, Giambattista Giacomin, Chien-Hao Huang, Maha Khatib, Hubert Lacoin, Alexandre Legrand, Brune Massoulié, Julien Poisat, Rémy Poudevigne-Auboiron, Christophe Sabot, Michele Salvi, Rongfeng Sun, Camille Tardif, Fabio L. Toninelli, Niccolò Torri, Ran Wei, Linglong Yuan, Nikos Zygouras.
My publications are listed below, classified by topic (and by anti-choronological order below).
All preprint versions are available on arXiv, or on HAL. Here is my Google Scholar profile.
  1. Q. Berger, C. Chong, H. Lacoin,
    The Stochastic Heat Equation with multiplicative Lévy noise: Existence, moments, and intermittency,
    Commun. Math. Phys., Vol. 402 (2023), pp. 2215–2299.
    [Journal] [arXiv]
  2. Q. Berger, H. Lacoin,
    The continuum directed polymer in Lévy Noise,
    J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
    [Journal] [arXiv]
  1. Q. Berger, A. 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. Q. Berger, C.-H. Huang, N. Torri, R. Wei,
    One-dimensional polymers in random environments: stretching vs. folding,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-45.
    [Journal] [arXiv]
  3. Q. Berger, N. Torri, R. 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. Q. Berger, H. 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. Q. Berger, N. Torri,
    Directed polymers in heavy-tail random environment,
    Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
    [Journal] [arXiv]
  6. Q. Berger, H. 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. Q. Berger, B. 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]
  2. Q. Berger, G. Giacomin, H. 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]
  3. K. S. Alexander, Q. Berger,
    Pinning of a renewal on a quenched renewal,
    Electron. J. Probab., Vol. 23 (2018), no 6, 48 pp.
    [Journal] [arXiv]
  4. Q. Berger, H. 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]
  5. Q. Berger, J. 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]
  6. Q. 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]
  7. Q. Berger, F. Caravenna, J. Poisat, R. Sun, N. 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]
  8. Q. 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]
  9. Q. Berger, F. Toninelli,
    Hierachical pinning model in correlated random environment,
    Ann. Inst. Henri Poincaré Probab. Stat., Vol. 48 Num. 3 (2013) 781-816.
    [Journal] [arXiv]
  10. Q. Berger, H. Lacoin,
    Sharp critical behavior for random pinning model with correlated environment,
    Stochastic Process. Appl., Vol. 122, Issue 4 (2012) 1397-1436.
    [Journal] [arXiv]
  11. Q. Berger, H. 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]
  12. Q. Berger, F. 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. Q. Berger, A. 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. Q. Berger, G. Giacomin, M. Khatib,
    Disorder and denaturation transition in the generalized Poland-Scheraga model,
    Ann. Henri Lebesgue, Vol. 3 (2020), pp. 299-339.
    [Journal] [arXiv]
  3. Q. Berger, G. Giacomin, M. 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. Q. Berger, F. den Hollander, J. 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. Q. Berger, N. Bouchot,
    Some properties of the principal Dirichlet eigenfunction via simple random walk and Brownian motion couplings,
    arXiv:2408.15858v2 [math.PR]
  2. Q. Berger, L. Béthencourt, C. Tardif,
    On joint returns to zero of Bessel processes,
    arXiv:2406.19344 [math.PR]
  3. Q. Berger, L. Béthencourt, C. Tardif,
    Persistence problems for additive functionals of one-dimensional Markov processes ,
    arXiv:2304.09034 [math.PR]
  4. Q. Berger, L. Béthencourt,
    An application of Sparre Andersen's fluctuation theorem for exchangeable and sign-invariant random variables,
    to appear in Séminaire de Probabilités, arXiv:2304.09031 [math.PR]
  5. Q. Berger, M. Birkner, L. Yuan,
    Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon,
    to appear in Ann. Fac. Sci. Toulouse.
    arXiv:2303.12505 [math.PR]
  6. Q. 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. Q. 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. K. Alexander, Q. Berger,
    Local asymptotics for the first intersection of two independent renewals,
    Electron. J. Probab., Vol. 21 (2016), no 68, 1-20.
    [Journal] [arXiv]
  9. K. Alexander, Q. Berger,
    Local limit theorem and renewal theory with no moments,
    Electron. J. Probab., Vol. 21 (2016), no 66, 1-18.
    [Journal] [arXiv]
  1. Q. Berger, N. 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. Q. Berger, N. Torri,
    Entropy-controlled Last-Passage Percolation,
    Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
    [Journal] [arXiv]
  3. K. S. Alexander, Q. Berger,
    Geodesics Toward Corners in First Passage Percolation,
    J. Stat. Phys., Vol. 172, Issue 4 (2018), pp 1029-1056.
    [Journal] [arXiv]
  1. Q. Berger, M. 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. Q. Berger, M. 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. I. Ayuso Ventura, Q. Berger,
    Non-linear conductances of Galton-Watson trees and application to the (near) critical random cluster model,
    arXiv:2404.11564 [math.PR]
  2. I. Ayuso Ventura, Q. 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

  • Q. 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]
  • Q. 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. Q. Berger, A. 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. Q. Berger, N. Bouchot,
    Some properties of the principal Dirichlet eigenfunction via simple random walk and Brownian motion couplings,
    arXiv:2408.15858v2 [math.PR]
  3. Q. Berger, L. Béthencourt, C. Tardif,
    On joint returns to zero of Bessel processes,
    arXiv:2406.19344 [math.PR]
  4. I. Ayuso Ventura, Q. Berger,
    Non-linear conductances of Galton-Watson trees and application to the (near) critical random cluster model,
    arXiv:2404.11564 [math.PR]
  5. Q. Berger, L. Béthencourt, C. Tardif,
    Persistence problems for additive functionals of one-dimensional Markov processes,
    arXiv:2304.09034 [math.PR]

    6. To appear

  6. Q. Berger, L. Béthencourt,
    An application of Sparre Andersen's fluctuation theorem for exchangeable and sign-invariant random variables,
    to appear in Séminaire de Probabilités.
    arXiv:2304.09031 [math.PR]
  7. Q. Berger, M. Birkner, L. Yuan,
    Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon,
    to appear in Ann. Fac. Sci. Toulouse.
    arXiv:2303.12505 [math.PR]

    8. 2025

  8. Q. 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]

    9. 2024

  9. I. Ayuso Ventura, Q. 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]
  10. Q. Berger, A. 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]
  11. Q. Berger, B. 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]

    12. 2023

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

    13. 2022

  13. Q. Berger, C.-H. Huang, N. Torri, R. Wei,
    One-dimensional polymers in random environments: stretching vs. folding,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-45.
    [Journal] [arXiv]
  14. Q. Berger, N. Torri, R. Wei,
    Non-directed polymers in heavy-tail random environment in dimension d≥2,
    Electron. J. Probab., Vol. 27 (2022), pp. 1-67.
    [Journal] [arXiv]
  15. Q. Berger, H. Lacoin,
    The continuum directed polymer in Lévy Noise,
    J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
    [Journal] [arXiv]

    16. 2021

  16. Q. Berger, H. Lacoin,
    The scaling limit of the directed polymer with power-law tail disorder,
    Commun. Math. Phys., Vol. 386 (2021), pp. 1051-1105.
    [Journal] [arXiv]
  17. Q. Berger, N. 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]

    18. 2016-2020

  18. Q. Berger, M. 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]
  19. Q. Berger, G. Giacomin, M. Khatib,
    Disorder and denaturation transition in the generalized Poland-Scheraga model,
    Ann. Henri Lebesgue, Vol. 3 (2020), pp. 299-339.
    [Journal] [arXiv]
  20. Q. 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]
  21. Q. Berger, N. Torri,
    Entropy-controlled Last-Passage Percolation,
    Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
    [Journal] [arXiv]
  22. Q. Berger, N. Torri,
    Directed polymers in heavy-tail random environment,
    Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
    [Journal] [arXiv]
  23. Q. Berger, G. Giacomin, H. 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]
  24. Q. Berger, M. 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]
  25. Q. 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]
  26. K. S. Alexander, Q. Berger,
    Geodesics Toward Corners in First Passage Percolation,
    J. Stat. Phys., Vol. 172, Issue 4 (2018), pp 1029-1056.
    [Journal] [arXiv]
  27. Q. Berger, F. den Hollander, J. 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]
  28. Q. Berger, G. Giacomin, M. 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]
  29. K. S. Alexander, Q. Berger,
    Pinning of a renewal on a quenched renewal,
    Electron. J. Probab., Vol. 23 (2018), no 6, 48 pp.
    [Journal] [arXiv]
  30. Q. Berger, H. 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]
  31. Q. Berger, H. 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]
  32. K. Alexander, Q. Berger,
    Local limit theorem and renewal theory with no moments,
    Electron. J. Probab., Vol. 21 (2016), no 66, 1-18.
    [Journal] [arXiv]
  33. K. Alexander, Q. Berger,
    Local asymptotics for the first intersection of two independent renewals,
    Electron. J. Probab., Vol. 21 (2016), no 68, 1-20.
    [Journal] [arXiv]

    34. before 2015

  34. Q. Berger, J. 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]
  35. Q. 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]
  36. Q. 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]
  37. Q. Berger, F. Caravenna, J. Poisat, R. Sun, N. 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]
  38. Q. 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]
  39. Q. Berger, F. Toninelli,
    Hierachical pinning model in correlated random environment,
    Ann. Inst. Henri Poincaré Probab. Stat., Vol. 48 Num. 3 (2013) 781-816.
    [Journal] [arXiv]
  40. Q. Berger, H. Lacoin,
    Sharp critical behavior for random pinning model with correlated environment,
    Stochastic Process. Appl., Vol. 122, Issue 4 (2012) 1397-1436.
    [Journal] [arXiv]
  41. Q. Berger, H. 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]
  42. Q. Berger, F. 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]