Hubert Lacoin

Publications

You can find below a list of publications and preprints classified by research topic and links to my co-authors webpage.
Quentin Berger, Charles Bordenave , Thierry Bodineau, Pietro Caputo, Carsten Chong, Bernard Derrida, Giambattista Giacomin, Jonathan Hermon, Stefan Junk, Wolfgang König, Cyril Labbé, Rémi Leblond, Fabio Martinelli, Gregorio Moreno, Peter Mörters, Yuval Peres, Rémi Rhodes, Nadia Sidorova, François Simenhaus, Julien Sohier, Augusto Texeira, Fabio Toninelli, Johan Tykesson, Vincent Vargas and Shangjie Yang.



Pinning problems for surface models


[7] H. Lacoin, Solid-On-Solid interfaces with disordered pinning, Communication in Mathematical Physics 383 (2021) 489-536. arXiv:2003.00560 [math.PR].

[6] G. Giacomin. H. Lacoin, The disordered lattice free field pinning model approaching criticality, Annals of Probability 50 (2022) 1478-1537. arXiv:1912.10538 [math-ph].

[5] H. Lacoin, Wetting and layering for Solid-on-Solid II: Layering transitions, Gibbs states, and regularity of the free energy Journal de l'École Polytechnique, 7 (2020) 1-62. arXiv:1712.03736 [math-ph].

[4] H. Lacoin, Wetting and layering for Solid-on-Solid I: Identification of the wetting point and critical behavior, Communications in Mathematical Physics 362 (2018) 1007–1048. arXiv:1703.06162 [math-ph].

[3] G. Giacomin. H. Lacoin, Disorder and wetting transition: the pinned harmonic crystal in dimension three or larger, Annals of Applied Probability 28 (2018) 577-606. arXiv:1607.03859 [math-ph].

[2] H. Lacoin, Pinning and disorder relevance for the lattice Gaussian Free Field II: the two dimensional case, Annales Scientifiques de l'ENS 52 (2019) 1331-1401. arXiv:1512.05240 [math-ph].

[1] G. Giacomin. H. Lacoin, Pinning and disorder relevance for the lattice Gaussian free field, Journal of the European Mathematical Society 20 (2018) 199-258 arXiv:1501.07909 [math-ph].



Disordered Pinning in one dimension


[15] Q. Berger, G. Giacomin and H. Lacoin Disorder and critical phenomena: the α=0 copolymer model, Propability Theory and Related Fields 174 (2019), 787–819 arXiv:1712.02261 [math.PR].

[14] H. Lacoin, Marginal relevance for the γ-stable pinning model, in Stochastic dynamics out of equilibrium, Giacomin G., Olla S., Saada E., Spohn H., Stoltz G. (eds), Springer Proceedings in Mathematics and Statistics 282 (2019) 597–616. 1612.02389 [math.PR].

[13] H. Lacoin, J. Sohier Disorder relevance without Harris Criterion: the case of pinning model with γ-stable environment, Electronic Journal of Probabability 122 (2017), paper no. 50. 1610.06786 [math.PR].

[12] Q. Berger, H. Lacoin, Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift, Journal of the Institute of Mathematics of Jussieu 17 (2018) 305-346. arXiv:1503.07315 [math-ph].

[11] H. Lacoin, The rounding of the phase transition for disordered pinning with stretched exponential tails, Annals of Applied Probability 27 (2017) 917-943. arXiv:1405.6875 [math-ph]

[10] Q. Berger, H. Lacoin, Exact critical behavior for random pinning model with correlated environment, Stochastic Processes and Application, 122 (2012) 1397-1436. arXiv:1104.4969 [math-PR]

[9] 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, Journal of Statistical Physics 42 (2011) 322-341. arXiv:1007.5162v1 [math-ph]

[8]H. Lacoin, The martingale approach to disorder irrelevance for pinning models, Electronic Communications in Probability 15 (2010) 418-427. arXiv:1002.4752 [math.PR]

[7] G. Giacomin, H. Lacoin, F.L. Toninelli Disorder relevance at marginality and critical point shift, Annales de l'Institut Henri Poincaré 47 (2011) 148-175. arXiv:0906.1942 [math-ph]

[6] G. Giacomin, H. Lacoin, F.L. Toninelli Marginal relevance of disorder for pinning models, Communication on Pure and Applied Mathematics 63 (2010) 233-265. arXiv:0811.4723 [math.ph]

[5] H. Lacoin Hierarchical pinning model with site disorder: Disorder is marginally relevant, Probability Theory Related Fields 148 (2010) 159-175 . arXiv:0807.4864 [math.PR]

[4] H. Lacoin, F.L. Toninelli, A smoothing inequality for hierarchical pinning models Spin Glasses: Statics and Dynamics, A. Boutet de Monvel and A. Bovier (eds.), Progress in Probability 62 (2009) 271-178 . preprint

[3] T. Bodineau, G. Giacomin, H. Lacoin, F.L. Toninelli, Copolymers at selective interfaces: new bounds on the phase diagram, J. Statist. Phys. 132 (2008) 603-626 . arXiv:0803.1766 [math.PR]

[2] B. Derrida, G. Giacomin, H. Lacoin, F.L. Toninelli, Fractional moment bounds and disorder relevance for pinning models, Communication in Mathematical Physics 287 (2009) 867-887. arXiv:0712.2515 [math.PR]

[1] G. Giacomin, H. Lacoin, F.L. Toninelli, Hierarchical pinning models, quadratic maps and quenched disorder, Probability Theory Related Fields 147 (2010) 185-216. arXiv:0711.4649 [math.PR]



Stochastic PDEs


[1] Q. Berger, C. Chong and H. Lacoin, The stochastic heat equation with multiplicative Lévy noise: Existence, moments, and intermittency, Communications in Mathematical Physics 402 (2023) 2215–2299. arXiv:2111.07988 [math.PR].

Directed polymers and related models


[12] S.Junk, H. Lacoin, Strong disorder and very strong disorder are equivalent for directed polymers, (preprint) arXiv:2402.02562 [math.PR].

[11] Q. Berger, H. Lacoin, The scaling limit of the directed polymer with power-law tail disorder, Communications in Mathematical Physics 386 (2021) 1051-1105. arXiv:2010.09592 [math.ph].

[10] Q. Berger, H. Lacoin, The continuum directed polymer in Lévy Noise, Journal de l’École polytechnique — Mathématiques, 9 (2022) 213-280. arXiv:2007.06484 [math.PR].

[9] Q. Berger, H. Lacoin, The high-temperature behavior for the directed polymer in dimension 1+2 Annales de l'Institut Henri Poincaré 52 (2017), 430-450. arXiv:1506.09055 [math.ph].

[8] H. Lacoin, Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster Journal of Statistical Physics, 154 (2014) 1461-1482 arXiv:1212.4641 [math.PR].

[7] H. Lacoin, Non-coincidence of Quenched and Annealed Connective Constants on the supercritical planar percolation cluster, Probability Theory and Related Fields 159 (2014) 777-808. arXiv:1203.6051 [math.PR].

[6] H. Lacoin, Existence of an intermediate phase for oriented percolation, Electronic Journal of Probability 17 (2012) 41, 1-17 arXiv:1201.4552 [math.PR].

[5] H. Lacoin, Volume exponent for Brownian Motion in a Poissonian Potential with long range correlation II: The Upper Bound, Annales de l'Institut Henri Poincaré. 48 (2012) 1029-1048. arXiv:1107.1106 [math-PR]

[4] H. Lacoin, Volume exponent for Brownian Motion in a Poissonian Potential with long range correlation I: The Lower bound, Annales de l'Institut Henri Poincaré 48 (2012) 1010-1028. arXiv:1104.1944 [math-PR]

[3] H. Lacoin, Influence of spatial correlation for directed polymers, Annals of probability 39 (2011) 139-175. arXiv:0912.3732 [math.ph]

[2] H. Lacoin, G. Moreno Directed Polymers on Hierarchical Lattices with site disorder, Stochastic Processes and Application 120 (2010) 467-493. arXiv:0906.0992 [math.PR]

[1] H. Lacoin, New bounds for the free energy of directed polymer in dimension 1+1 and 1+2, Communications in Mathematical Physics 294 (2010) 471-503. arXiv:0901.0699 [math.ph]



Markov chain mixing time


[13] P. Caputo, C. Labbé, H. Lacoin, Cutoff phenomenon in nonlinear recombinations, (preprint) arXiv:2402.11396 [math.PR].


[12] H. Lacoin, Mixing time and cutoff for one dimensional particle systems, Proceedings of the 29th International Congress of Mathematicians (2022) 4350-4374. arXiv:2007.10108 [math.PR].


[11] P. Caputo, C. Labbé, H. Lacoin, Spectral gap and cutoff phenomenon for the Gibbs sampler of Nabla-Phi interfaces with convex potential, Annales de l'Institut Henri Poincare (B) Probabilites et statistiques 58 (2022) 794-826 arXiv:2007.10108 [math.PR].


[10] P. Caputo, C. Labbé, H. Lacoin, Mixing time of the adjacent walk on the simplex, Annals of Probability 48 (2020) 2449-2493. arXiv:1904.01088 [math.PR].


[9] C. Bordenave, H. Lacoin, Cutoff at the entropic time for random walks on covered expander graphs, Journal of the Institute of Mathematics of Jussieu 21 (2022) 1571-1616. arXiv:1805.12213 [math.PR].


[8] C. Labbé, H. Lacoin, Mixing time and cutoff for the weakly asymmetric simple exclusion process, Annals of Applied Probability 30 (2020) 1847-1883. arXiv:1805.12213 [math.PR].


[7] C. Labbé, H. Lacoin, Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling, Annals of Probability 47 (2019), 1541-1586. arXiv:1610.07383 [math.PR].


[6] J. Hermon, H. Lacoin, Y. Peres, Total Variation and Separation Cutoffs are not equivalent and neither one implies the other, Electronic Journal of Probability 21 (2016) paper no 44. arXiv:1508.03913 [math.PR]

[5] H. Lacoin,, The Cutoff profile for the Simple-Exclusion process on the circle, Annals of Probability 21 (2016) 3399-3430. arXiv:1502.00952 [math.PR]

[4] H. Lacoin,, A product chain without cutoff, Electronic Communication in Probability 20 (2015) paper no 19. arXiv:1407.1754 [math.PR]

[3] H. Lacoin,, The Simple Exclusion Process on the Circle has a diffusive Cutoff Window, Annales de l'Institut Henri Poincaré 53 (2017) 1402-1437. arXiv:1401.7296 [math.PR]

[2] H. Lacoin, Mixing time and Cutoff for the Adjacent Transposition shuffle and the simple exclusion, Annals of Probability 44 (2016) 1426-1487. arXiv:1309.3873 [math.PR]


[1] H. Lacoin, R. Leblond, The cutoff phenomenon for the simple exclusion process on the complete graph, ALEA, Latin American Journal of Probability and Statistics, 8 (2011) 285-301. arXiv:1010.4866 [math-PR]


Gaussian multiplicative chaos


[10] H. Lacoin, Critical Gaussian Multiplicative Chaos for singular measures (preprint) arXiv:2304.05781 [math.PR]

[9] H. Lacoin, Convergence for Complex Gaussian Multiplicative Chaos on phase boundaries to appear in Probability and Mathematical Physics arXiv:2301.05274 [math.PR]

[8] H. Lacoin, Critical Gaussian Multiplicative Chaos revisited to appear in Annales de l'Institut Henri Poincaré arXiv:2209.06683 [math.PR]

[7] H. Lacoin, Convergence in law for Complex Gaussian Multiplicative Chaos in phase III Annals of Probability 50 (2022) 950-983. arXiv:2011.08033 [math.PR]

[6] H. Lacoin, A universality result for subcritical Complex Gaussian Multiplicative Chaos, Annals of Applied Probability >32 (2022) 269-293 arXiv:2003.14024 [math.PR]

[5] H. Lacoin, R. Rhodes, V. Vargas, The semiclassical limit of Liouville conformal field theory, Annales de la faculté des sciences de Toulouse 31 (2022) 1031–1083. arXiv:1903.08883 [math.PR]

[4] H. Lacoin, R. Rhodes, V. Vargas , A probabilistic approach of ultraviolet renormalisation in the boundary Sine-Gordon model, Probability Theory and Related Fields 171 (2022), 1-40 arXiv:1903.01394 [math.PR]

[3] H. Lacoin, R. Rhodes, V. Vargas, Path integral for quantum Mabuchi K-energy, Duke Mathematical Journal 171 (2022) 483-545. arXiv:1807.01758 [math.PR]

[2] H. Lacoin, R. Rhodes, V. Vargas, Semiclassical limit of Liouville Field Theory, Journal of Functional Analysis 273 (2017) 875-916. arXiv:1401.6001 [math.PR]

[1] H. Lacoin, R. Rhodes, V. Vargas, Complex Gaussian Multiplicative Chaos, Communications in Mathematical Physics 337 (2015) 569–632. arXiv:1307.6117 [math.PR]



Out of equilibrium dynamics


[9] H. Lacoin, S. Yang, Mixing time for the asymmetric simple exclusion process in a random environment, Annals of Applied Probability 34 (2024) 388-427. arXiv:2102.02606 [math.PR]

[8] H. Lacoin, S. Yang, Metastability for expanding bubbles on a sticky substrate Annals of Applied Probability 32 (2022) 3408-3449. arXiv:2007.07832 [math.PR]

[7] H. Lacoin, A. Teixeira, A mathematical perspective on metastable wetting, Electronic Journal of Probability 20 (2015) paper no 17. arXiv:1312.7732 [math.PR]

[6] H. Lacoin, F. Simenhaus, F.L. Toninelli, The heat equation shrinks Ising droplets to points, Communication on Pure and Applied Mathematics 68 (2015) 1640–1681. 1306.4507 [math-ph]

[5] H. Lacoin, The scaling limit for zero temperature planar Ising droplets: with and without magnetic fields, Topics in percolative and disordered systems, Springer Proceedings in Mathematics & Statistics 69 (2014) 85-120. 1210.2597 [math-PR]

[4] H. Lacoin, The scaling limit of polymer pinning dynamics and a one dimensional Stefan freezing problem, Communication in Mathematical Physics 331 (2014) 21-66. arXiv:1204.1253 [math-ph]

[3] H. Lacoin, F. Simenhaus, F.L. Toninelli, Zero-temperature stochastic Ising model in two Dimension and anisotropic curve-shortening flow, Journal of The European Mathematical Society 16 (2014) 2557-2615. arXiv:1112.3160 [math-ph]

[2] H. Lacoin, Approximate Lifshitz law for zero-temperature Ising model in any dimension, Communication in Mathematical Physics 318 (2013) 291-305. arXiv:1102.3466 [math-ph]

[1] P. Caputo, H. Lacoin, F. Martinelli, F. Simenhaus ,F.L. Toninelli, Polymer dynamics in the depinned phase: metastability with logarithmic barriers, Probability Theory and Related Fields 153 (2012) 587-641. arXiv:1007.4470 [math.PR]



Parabolic Anderson Model


[2] H. Lacoin, P. Mörters, A scaling limit theorem for the parabolic Anderson model with exponential potential, Probability in Complex Physical Systems, Springer Proceedings in Mathematics 11 (2011) 247-272 arXiv:1009.4862v1 [math.PR]

[1] W. Koenig, H. Lacoin, P. Moerters, N. Sidorova A Two city theorem for the parabolic Anderson model, Annals of Probability 37 (2009) 347-392. arXiv:1102.4921 [math.PR]



Random Interlacements


[1] H. Lacoin, J. Tykesson , On the easiest way to link k points in the random interlacement process, ALEA, Latin American Journal of Probability and Statistics 10 (2013) 505-524. arXiv:1206.4216 [math.PR]