2025
Periodic space-time homogenisation of the φ24 equation
JOURNAL OF FUNCTIONAL ANALYSIS. 2025. Vol. 288, num. 5. DOI : 10.1016/j.jfa.2024.110762.2024
Singularity of solutions to singular SPDEs
2024
Scaling limit of the KPZ equation with non-integrable spatial correlations
2024
Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise
Annals Of Pde. 2024. Vol. 10, num. 1, p. 3. DOI : 10.1007/s40818-023-00165-6.Stochastic quantisation of Yang-Mills-Higgs in 3D
INVENTIONES MATHEMATICAE. 2024. Vol. 237, num. 2, p. 541 – 696. DOI : 10.1007/s00222-024-01264-2.The BPHZ Theorem for Regularity Structures via the Spectral Gap Inequality
Archive For Rational Mechanics And Analysis. 2024. Vol. 248, num. 1, p. 9. DOI : 10.1007/s00205-023-01946-w.Renormalisation in the presence of variance blowup
2024
2023
Periodic space-time homogenisation of the $φ^4_2$ equation
2023
Lp-regularity theory for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity
Journal Of Differential Equations. 2023. Vol. 379, p. 569 – 599. DOI : 10.1016/j.jde.2023.10.042.Directed mean curvature flow in noisy environment
Communications On Pure And Applied Mathematics. 2023. Vol. 77, num. 3, p. 1850 – 1939. DOI : 10.1002/cpa.22158.A scaling limit of the parabolic Anderson model with exclusion interaction
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2023. Vol. 77, num. 2, p. 1065 – 1125. DOI : 10.1002/cpa.22145.Regularity Structures on Manifolds and Vector Bundles
2023
A Stroll Around The Critical Potts Model
Bulletin Of The American Mathematical Society. 2023. DOI : 10.1090/bull/1802.Spectral gap for projective processes of linear SPDEs
2023
A Dynamical Yukawa$_{2}$ Model
2023
The Allen-Cahn equation with generic initial datum
Probability Theory And Related Fields. 2023. DOI : 10.1007/s00440-023-01198-5.Fluctuations of stochastic PDEs with long-range correlations
2023
The Brownian Web as a random R-tree
Electronic Journal Of Probability. 2023. Vol. 28. DOI : 10.1214/23-EJP984.THE COMPACT SUPPORT PROPERTY FOR SOLUTIONS TO THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH COLORED NOISE
Siam Journal On Mathematical Analysis. 2023. Vol. 55, num. 6, p. 7665 – 7703. DOI : 10.1137/23M1557283.2022
The Brownian Castle
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2022. Vol. 76, num. 10, p. 2693 – 2764. DOI : 10.1002/cpa.22085.Boundary renormalisation of SPDEs
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 2022. Vol. 47, num. 10, p. 2070 – 2123. DOI : 10.1080/03605302.2022.2109173.Generating Diffusions with Fractional Brownian Motion
COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2022. Vol. 396, num. 1, p. 91 – 141. DOI : 10.1007/s00220-022-04462-2.The work of Hugo Duminil-Copin
2022
Langevin dynamic for the 2D Yang-Mills measure
PUBLICATIONS MATHEMATIQUES DE L IHES. 2022. Vol. 136, num. 1, p. 1 – 147. DOI : 10.1007/s10240-022-00132-0.The Φ34 Measure Has Sub-Gaussian Tails
JOURNAL OF STATISTICAL PHYSICS. 2022. Vol. 186, num. 3. DOI : 10.1007/s10955-021-02866-3.The support of singular stochastic partial differential equations
FORUM OF MATHEMATICS PI. 2022. Vol. 10. DOI : 10.1017/fmp.2021.18.Geometric Stochastic Heat Equations
Journal Of The American Mathematical Society. 2022. Vol. 35, num. 1, p. 1 – 80. DOI : 10.1090/jams/977.2021
A Noise-Induced Transition in the Lorenz System
COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2021. Vol. 383, num. 3, p. 2243 – 2274. DOI : 10.1007/s00220-021-04000-6.Renormalising SPDEs in regularity structures
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. 2021. Vol. 23, num. 3, p. 869 – 947. DOI : 10.4171/JEMS/1025.2020
Fluctuations Around a Homogenised Semilinear Random PDE
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. 2020. Vol. 239, num. 1, p. 151 – 217. DOI : 10.1007/s00205-020-01574-8.AVERAGING DYNAMICS DRIVEN BY FRACTIONAL BROWNIAN MOTION
ANNALS OF PROBABILITY. 2020. Vol. 48, num. 4, p. 1826 – 1860. DOI : 10.1214/19-AOP1408.2019
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2019.LARGE SCALE LIMIT OF INTERFACE FLUCTUATION MODELS
ANNALS OF PROBABILITY. 2019. Vol. 47, num. 6, p. 3478 – 3550. DOI : 10.1214/18-AOP1317.Discretisation of regularity structures
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2019. Vol. 55, num. 4, p. 2209 – 2248. DOI : 10.1214/18-AIHP947.A Solution Theory for Quasilinear Singular SPDEs
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2019. Vol. 72, num. 9, p. 1983 – 2005. DOI : 10.1002/cpa.21816.Singular SPDEs in domains with boundaries
PROBABILITY THEORY AND RELATED FIELDS. 2019. Vol. 173, num. 3-4, p. 697 – 758. DOI : 10.1007/s00440-018-0841-1.Algebraic renormalisation of regularity structures
INVENTIONES MATHEMATICAE. 2019. Vol. 215, num. 3, p. 1039 – 1156. DOI : 10.1007/s00222-018-0841-x.Hormander’s theorem for semilinear SPDEs
ELECTRONIC JOURNAL OF PROBABILITY. 2019. Vol. 24. DOI : 10.1214/19-EJP387.2018
A CLASS OF GROWTH MODELS RESCALING TO KPZ
FORUM OF MATHEMATICS PI. 2018. Vol. 6. DOI : 10.1017/fmp.2018.2.Renormalisation of parabolic stochastic PDEs
JAPANESE JOURNAL OF MATHEMATICS. 2018. Vol. 13, num. 2, p. 187 – 233. DOI : 10.1007/s11537-018-1742-x.The dynamical sine-Gordon model in the full subcritical regime
2018
The strong Feller property for singular stochastic PDEs
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2018. Vol. 54, num. 3, p. 1314 – 1340. DOI : 10.1214/17-AIHP840.Tightness of the Ising-Kac Model on the Two-Dimensional Torus
JOURNAL OF STATISTICAL PHYSICS. 2018. Vol. 171, num. 4, p. 632 – 655. DOI : 10.1007/s10955-018-2033-x.DISCRETISATIONS OF ROUGH STOCHASTIC PDES
ANNALS OF PROBABILITY. 2018. Vol. 46, num. 3, p. 1651 – 1709. DOI : 10.1214/17-AOP1212.Large-Scale Behavior of Three-Dimensional Continuous Phase Coexistence Models
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2018. Vol. 71, num. 4, p. 688 – 746. DOI : 10.1002/cpa.21738.A FRACTIONAL KINETIC PROCESS DESCRIBING THE INTERMEDIATE TIME BEHAVIOUR OF CELLULAR FLOWS
ANNALS OF PROBABILITY. 2018. Vol. 46, num. 2, p. 897 – 955. DOI : 10.1214/17-AOP1196.Non-equilibrium steady states for networks of oscillators
Electronic Journal of Probability. 2018. Vol. 23, num. 55, p. 1 – 28. DOI : 10.1214/18-EJP177.WEAK ERROR ESTIMATES FOR TRAJECTORIES OF SPDEs UNDER SPECTRAL GALERKIN DISCRETIZATION
JOURNAL OF COMPUTATIONAL MATHEMATICS. 2018. Vol. 36, num. 2, p. 159 – 182. DOI : 10.4208/jcm.1607-m2016-0539.Multiplicative stochastic heat equations on the whole space
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. 2018. Vol. 20, num. 4, p. 1005 – 1054. DOI : 10.4171/JEMS/781.An analyst’s take on the BPHZ theorem
2018. The Abel Symposium, Rosendal, Norway, 2016-08-16 – 2016-08-19. p. 429 – 476. DOI : 10.1007/978-3-030-01593-0_16.2017
A CENTRAL LIMIT THEOREM FOR THE KPZ EQUATION
ANNALS OF PROBABILITY. 2017. Vol. 45, num. 6B, p. 4167 – 4221. DOI : 10.1214/16-AOP1162.The reconstruction theorem in Besov spaces
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An analytic BPHZ theorem for regularity structures
2016
From averaging to homogenization in cellular flows – An exact description of the transition
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Stochastics and Partial Differential Equations: Analysis and Computations. 2016. Vol. 4, num. 2, p. 402 – 437. DOI : 10.1007/s40072-015-0067-5.The motion of a random string
2016
The Dynamical Sine-Gordon Model
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2016
2015
A Wong-Zakai theorem for stochastic PDEs
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2015
A simple construction of the continuum parabolic Anderson model on R2
ELECTRONIC COMMUNICATIONS IN PROBABILITY. 2015. Vol. 20, p. 1 – 11. DOI : 10.1214/ECP.v20-4038.Introduction to regularity structures
BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS. 2015. Vol. 29, num. 2, p. 175 – 210. DOI : 10.1214/14-BJPS241.LOSS OF REGULARITY FOR KOLMOGOROV EQUATIONS
ANNALS OF PROBABILITY. 2015. Vol. 43, num. 2, p. 468 – 527. DOI : 10.1214/13-AOP838.Geometric versus non-geometric rough paths
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2015. Vol. 51, num. 1, p. 207 – 251. DOI : 10.1214/13-AIHP564.Exponential ergodicity for Markov processes with random switching
BERNOULLI. 2015. Vol. 21, num. 1, p. 505 – 536. DOI : 10.3150/13-BEJ577.The Brownian Fan
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SPECTRAL GAPS FOR A METROPOLIS-HASTINGS ALGORITHM IN INFINITE DIMENSIONS
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2014
2013
Random homogenisation of a highly oscillatory singular potential
Stochastics and Partial Differential Equations: Analysis and Computations. 2013. Vol. 1, num. 4, p. 571 – 605. DOI : 10.1007/s40072-013-0018-y.Solving the KPZ equation
ANNALS OF MATHEMATICS. 2013. Vol. 178, num. 2, p. 559 – 664. DOI : 10.4007/annals.2013.178.2.4.REGULARITY OF LAWS AND ERGODICITY OF HYPOELLIPTIC SDES DRIVEN BY ROUGH PATHS
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PROBABILITY THEORY AND RELATED FIELDS. 2013. Vol. 155, num. 1-2, p. 71 – 126. DOI : 10.1007/s00440-011-0392-1.Nonasymptotic mixing of the MALA algorithm
IMA JOURNAL OF NUMERICAL ANALYSIS. 2013. Vol. 33, num. 1, p. 80 – 110. DOI : 10.1093/imanum/drs003.2012
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ELECTRONIC JOURNAL OF PROBABILITY. 2012. Vol. 17, p. 1 – 38. DOI : 10.1214/EJP.v17-1807.A SPATIAL VERSION OF THE ITO-STRATONOVICH CORRECTION
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PROBABILITY THEORY AND RELATED FIELDS. 2012. Vol. 152, num. 1-2, p. 265 – 297. DOI : 10.1007/s00440-010-0322-7.2011
Approximations to the Stochastic Burgers Equation
JOURNAL OF NONLINEAR SCIENCE. 2011. Vol. 21, num. 6, p. 897 – 920. DOI : 10.1007/s00332-011-9104-3.Rough Stochastic PDEs
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BULLETIN DES SCIENCES MATHEMATIQUES. 2011. Vol. 135, num. 6-7, p. 650 – 666. DOI : 10.1016/j.bulsci.2011.07.007.A chain of interacting particles under strain
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ANNALS OF APPLIED PROBABILITY. 2011. Vol. 21, num. 2, p. 669 – 698. DOI : 10.1214/10-AAP708.PERIODIC HOMOGENIZATION WITH AN INTERFACE: THE MULTI-DIMENSIONAL CASE
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Electronic Journal of Probability. 2011. Vol. 16, p. 658 – 738. DOI : 10.1214/EJP.v16-875.2010
Periodic homogenization with an interface: The one-dimensional case
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2010. 7th International ISAAC Congress, Imperial College London, UK, 2009-07-13 – 2009-07-18. p. 479 – 484. DOI : 10.1142/9789814313179_0062.A simple framework to justify linear response theory
NONLINEARITY. 2010. Vol. 23, num. 4, p. 909 – 922. DOI : 10.1088/0951-7715/23/4/008.2009
How Hot Can a Heat Bath Get?
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Probability Theory and Related Fields. 2009. Vol. 146, num. 1, p. 1 – 47. DOI : 10.1007/s00440-008-0182-6.Slow energy dissipation in anharmonic oscillator chains
Communications on Pure and Applied Mathematics. 2009. Vol. 62, num. 8, p. 999 – 1032. DOI : 10.1002/cpa.20280.An Introduction to Stochastic PDEs
2009
Asymptotic coupling and a weak form of Harris’ theorem with applications to stochastic delay equations
2009
Ergodic properties of a class of non-Markovian processes
2009
2008
SPECTRAL GAPS IN WASSERSTEIN DISTANCES AND THE 2D STOCHASTIC NAVIER-STOKES EQUATIONS
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2008
Ornstein-Uhlenbeck processes on Lie groups
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A version of Hormander’s theorem for the fractional Brownian motion
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ANNALS OF APPLIED PROBABILITY. 2007. Vol. 17, num. 5-6, p. 1657 – 1706. DOI : 10.1214/07-AAP441.Ergodic theory for sdes with extrinsic memory
ANNALS OF PROBABILITY. 2007. Vol. 35, num. 5, p. 1950 – 1977. DOI : 10.1214/009117906000001141.Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities
NONLINEARITY. 2007. Vol. 20, num. 7, p. 1721 – 1744. DOI : 10.1088/0951-7715/20/7/009.Sampling the posterior: An approach to non-Gaussian data assimilation
Physica D: Nonlinear Phenomena. 2007. Vol. 230, num. 1-2, p. 50 – 64. DOI : 10.1016/j.physd.2006.06.009.2006
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2006
Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
Annals of Mathematics. 2006. Vol. 164, num. 3, p. 993 – 1032. DOI : 10.4007/annals.2006.164.993.2005
Modulation equations: Stochastic bifurcation in large domains
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2005
A probabilistic argument for the controllability of conservative systems
2005
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Communications in Mathematical Sciences. 2005. Vol. 3, num. 4, p. 587 – 603. DOI : 10.4310/CMS.2005.v3.n4.a8.2004
Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations
COMPTES RENDUS MATHEMATIQUE. 2004. Vol. 339, num. 12, p. 879 – 882. DOI : 10.1016/j.crma.2004.09.035.Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations
COMPTES RENDUS MATHEMATIQUE. 2004. Vol. 339, num. 11, p. 793 – 796. DOI : 10.1016/j.crma.2004.09.002.Multiscale expansion of invariant measures for SPDEs
COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2004. Vol. 251, num. 3, p. 515 – 555. DOI : 10.1007/s00220-004-1130-7.Periodic homogenization for hypoelliptic diffusions
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2004