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, polymers, phase transition, critical phenomena, influence of disorder, random walks, renewal processes, first-passage percolation, last-passage percolation...



Publications and preprints:


Here is a list of my collaborators (by chronological order): Fabio L. Toninelli, Hubert Lacoin, Francesco Caravenna, Julien Poisat, Rongfeng Sun, Nikos Zygouras, Kenneth S. Alexander, Giambattista Giacomin, Maha Khatib, Frank den Hollander, Michele Salvi, Niccolò Torri, Chien-Hao Huang, Ran Wei.
My publications are listed below, classified by topic. All preprint versions are available on arXiv, or on HAL. Here is my Google Scholar profile.

  1. Q. Berger, N. Torri, R. Wei, Non-directed polymers in heavy-tail random environment in dimension d≥2, arXiv:2101.05949 [math.PR]

  2. Q. Berger, H. Lacoin, The continuum directed polymer in Lévy Noise, arXiv:2007.06484 [math.PR]

  3. Q. Berger, C.-H. Huang, N. Torri, R. Wei, One-dimensional polymers in random environments: stretching vs. folding, arXiv:2002.06899 [math.PR]

  4. Q. Berger, H. Lacoin, The scaling limit of the directed polymer with power-law tail disorder, Commun. Math. Phys. (2021), online first. [Journal] [arXiv]

  5. Q. Berger, N. Torri, Directed polymers in heavy-tail random environment, Ann. Probab., Vol. 47, Num. 6, pp. 4024-4076 (2019).
    [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, G. Giacomin, H. Lacoin, Disorder and critical phenomena: the α=0 copolymer model, Probab. Theory Relat. Fields, Vol. 174, Issue 3-4, pp. 787–819 (2019).
    [Journal] [arXiv]

  2. 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]

  3. 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]

  4. 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]

  5. 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]

  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]


  1. Q. Berger, G. Giacomin, M. Khatib, Disorder and denaturation transition in the generalized Poland-Scheraga model, Ann. Henri Lebesgue, Vol. 3, pp. 299-339 (2020).
    [Journal] [arXiv]

  2. Q. Berger, G. Giacomin, M. Khatib, DNA melting structures in the generalized Poland-Scheraga model, ALEA, Lat. Am. J. Probab. Math. Stat., Vol. 15, pp 993-1025 (2018).
    [Journal] [arXiv]


  1. Q. Berger, Notes on Random Walks in the Cauchy domain of attraction, Probab. Theory Relat. Fields, Vol. 175, Issue 1-2, pp. 1-44 (2019).
    [Journal] [arXiv]

  2. Q. Berger, Strong renewal theorems and local large deviations for multivariate random walks and renewals, Electron. J. Probab., Vol. 24, no. 46, 47 pp (2019).
    [Journal] [arXiv]

  3. 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]

  4. 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., to appear.
    [arXiv]

  2. Q. Berger, N. Torri, Entropy-controlled Last-Passage Percolation, Ann. Appl. Probab., Vol. 29, Num. 3, pp 1878-1903 (2019).
    [Journal] [arXiv]

  3. K. S. Alexander, Q. Berger, Geodesics Toward Corners in First Passage Percolation, J. Stat. Phys., Vol. 172, Issue 4, pp 1029-1056 (2018).
    [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, 43 pp. (2020)
    [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, pp 171-187 (2019).
    [Journal] [arXiv]


  1. 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]

  2. 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, 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]


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.

Large audience articles