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.
-
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] -
Q. Berger, H. Lacoin,
The continuum directed polymer in Lévy Noise,
J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
[Journal] [arXiv]
-
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] -
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] -
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] -
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] -
Q. Berger, N. Torri,
Directed polymers in heavy-tail random environment,
Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
[Journal] [arXiv] -
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]
-
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] -
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] -
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] -
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] -
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] -
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] - 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] -
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] -
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] -
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] -
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] -
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]
-
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] -
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] -
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] -
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]
-
Q. Berger, N. Bouchot,
Some properties of the principal Dirichlet eigenfunction via simple random walk and Brownian motion couplings,
arXiv:2408.15858v2 [math.PR] -
Q. Berger, L. Béthencourt, C. Tardif,
On joint returns to zero of Bessel processes,
arXiv:2406.19344 [math.PR] -
Q. Berger, L. Béthencourt, C. Tardif,
Persistence problems for additive functionals of one-dimensional Markov processes ,
arXiv:2304.09034 [math.PR] -
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] -
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] -
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] -
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] -
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] -
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]
-
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] -
Q. Berger, N. Torri,
Entropy-controlled Last-Passage Percolation,
Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
[Journal] [arXiv] -
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]
-
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] -
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]
-
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] -
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, Modélisation aléatoire et stochastique - Journées MAS 2022. [PDF] -
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]
Large audience articles
-
Le paradoxe de Simpson illustré par des données de vaccination contre le Covid-19,
The conversation, 3 novembre 2021.
-
L'art et la manière de mélanger un paquet de cartes,
The conversation, 3 août 2020. -
Modèles de polymère, transition d'accrochage et désordre,
Matapli (SMAI) n°109, march 2016. (in French). [PDF]
Articles by anti-chronological order
-
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] -
Q. Berger, N. Bouchot,
Some properties of the principal Dirichlet eigenfunction via simple random walk and Brownian motion couplings,
arXiv:2408.15858v2 [math.PR] -
Q. Berger, L. Béthencourt, C. Tardif,
On joint returns to zero of Bessel processes,
arXiv:2406.19344 [math.PR] -
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] -
Q. Berger, L. Béthencourt, C. Tardif,
Persistence problems for additive functionals of one-dimensional Markov processes,
arXiv:2304.09034 [math.PR] -
Q. Berger, Céline Bonnet, Lucile Laulin, Kilian Raschel,
Topics in random walks,
ESAIM: Proceedings and Surveys, Modélisation aléatoire et stochastique - Journées MAS 2022.
[PDF] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
Q. Berger, H. Lacoin,
The continuum directed polymer in Lévy Noise,
J. Éc. Polytech., Tome 9 (2022), pp. 213-280.
[Journal] [arXiv] -
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] -
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] -
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] -
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] -
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] -
Q. Berger, N. Torri,
Entropy-controlled Last-Passage Percolation,
Ann. Appl. Probab., Vol. 29, Num. 3 (2019), pp. 1878-1903.
[Journal] [arXiv] -
Q. Berger, N. Torri,
Directed polymers in heavy-tail random environment,
Ann. Probab., Vol. 47, Num. 6 (2019), pp. 4024-4076.
[Journal] [arXiv] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] -
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] - 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] -
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] -
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] -
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] -
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] -
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]