Publications

2024

Singularity of solutions to singular SPDEs

M. Hairer; S. Kusuoka; H. Nagoji 

2024

Scaling limit of the KPZ equation with non-integrable spatial correlations

L. Gerolla; M. Hairer; X-M. Li 

2024

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

M. Hairer; T. Rosati 

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

A. Chandra; I. Chevyrev; M. Hairer; H. Shen 

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

M. Hairer; R. Steele 

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

M. Hairer 

2024

2023

Periodic space-time homogenisation of the $φ^4_2$ equation

M. Hairer; H. Singh 

2023

Lp-regularity theory for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity

B-S. Han; J. Yi 

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

A. Gerasimovics; M. Hairer; K. Matetski 

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

D. Erhard; M. Hairer 

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

M. Hairer; H. Singh 

2023

A Stroll Around The Critical Potts Model

M. Hairer 

Bulletin Of The American Mathematical Society. 2023. DOI : 10.1090/bull/1802.

Spectral gap for projective processes of linear SPDEs

M. Hairer; T. Rosati 

2023

A Dynamical Yukawa$_{2}$ Model

A. Chandra; M. Hairer; M. Peev 

2023

The Allen-Cahn equation with generic initial datum

M. Hairer; K. Le; T. Rosati 

Probability Theory And Related Fields. 2023. DOI : 10.1007/s00440-023-01198-5.

Fluctuations of stochastic PDEs with long-range correlations

L. Gerolla; M. Hairer; X-M. Li 

2023

The Brownian Web as a random R-tree

G. Cannizzaro; M. Hairer 

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

B-S. Han; K. Kim; J. Yi 

Siam Journal On Mathematical Analysis. 2023. Vol. 55, num. 6, p. 7665 – 7703. DOI : 10.1137/23M1557283.

2022

The Brownian Castle

G. Cannizzaro; M. Hairer 

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2022. Vol. 76, num. 10, p. 2693 – 2764. DOI : 10.1002/cpa.22085.

Boundary renormalisation of SPDEs

M. Gerencser; M. Hairer 

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

M. Hairer; X-M. Li 

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

M. Hairer 

2022

Langevin dynamic for the 2D Yang-Mills measure

A. Chandra; I. Chevyrev; M. Hairer; H. Shen 

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

M. Hairer; R. Steele 

JOURNAL OF STATISTICAL PHYSICS. 2022. Vol. 186, num. 3. DOI : 10.1007/s10955-021-02866-3.

The support of singular stochastic partial differential equations

M. Hairer; P. Schonbauer 

FORUM OF MATHEMATICS PI. 2022. Vol. 10. DOI : 10.1017/fmp.2021.18.

Geometric Stochastic Heat Equations

Y. Bruned; F. Gabriel; M. Hairer; L. Zambotti 

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

M. Coti Zelati; M. Hairer 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2021. Vol. 383, num. 3, p. 2243 – 2274. DOI : 10.1007/s00220-021-04000-6.

Renormalising SPDEs in regularity structures

Y. Bruned; A. Chandra; I. Chevyrev; M. Hairer 

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

M. Hairer; E. Pardoux 

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

M. Hairer; X-M. Li 

ANNALS OF PROBABILITY. 2020. Vol. 48, num. 4, p. 1826 – 1860. DOI : 10.1214/19-AOP1408.

2019

LARGE SCALE LIMIT OF INTERFACE FLUCTUATION MODELS

M. Hairer; W. Xu 

ANNALS OF PROBABILITY. 2019. Vol. 47, num. 6, p. 3478 – 3550. DOI : 10.1214/18-AOP1317.

Discretisation of regularity structures

D. Erhard; M. Hairer 

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

M. Gerencser; M. Hairer 

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

M. Gerencser; M. Hairer 

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

Y. Bruned; M. Hairer; L. Zambotti 

INVENTIONES MATHEMATICAE. 2019. Vol. 215, num. 3, p. 1039 – 1156. DOI : 10.1007/s00222-018-0841-x.

Hormander’s theorem for semilinear SPDEs

A. Gerasimovics; M. Hairer 

ELECTRONIC JOURNAL OF PROBABILITY. 2019. Vol. 24. DOI : 10.1214/19-EJP387.

2018

A CLASS OF GROWTH MODELS RESCALING TO KPZ

M. Hairer; J. Quastel 

FORUM OF MATHEMATICS PI. 2018. Vol. 6. DOI : 10.1017/fmp.2018.2.

Renormalisation of parabolic stochastic PDEs

M. Hairer 

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

A. Chandra; M. Hairer; H. Shen 

2018

The strong Feller property for singular stochastic PDEs

M. Hairer; J. Mattingly 

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

M. Hairer; M. Iberti 

JOURNAL OF STATISTICAL PHYSICS. 2018. Vol. 171, num. 4, p. 632 – 655. DOI : 10.1007/s10955-018-2033-x.

DISCRETISATIONS OF ROUGH STOCHASTIC PDES

M. Hairer; K. Matetski 

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

M. Hairer; W. Xu 

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

M. Hairer; G. Iyer; L. Koralov; A. Novikov; Z. Pajor-Gyulai 

ANNALS OF PROBABILITY. 2018. Vol. 46, num. 2, p. 897 – 955. DOI : 10.1214/17-AOP1196.

Non-equilibrium steady states for networks of oscillators

N. Cuneo; J. P. Eckmann; M. Hairer; L. Rey-Bellet 

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

C-E. Brehier; M. Hairer; A. M. Stuart 

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

M. Hairer; C. Labbe 

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

M. Hairer 

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

M. Hairer; H. Shen 

ANNALS OF PROBABILITY. 2017. Vol. 45, num. 6B, p. 4167 – 4221. DOI : 10.1214/16-AOP1162.

The reconstruction theorem in Besov spaces

M. Hairer; C. Labbe 

JOURNAL OF FUNCTIONAL ANALYSIS. 2017. Vol. 273, num. 8, p. 2578 – 2618. DOI : 10.1016/j.jfa.2017.07.002.

2016

An analytic BPHZ theorem for regularity structures

A. Chandra; M. Hairer 

2016

From averaging to homogenization in cellular flows – An exact description of the transition

M. Hairer; L. Koralov; Z. Pajor-Gyulai 

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2016. Vol. 52, num. 4, p. 1592 – 1613. DOI : 10.1214/15-AIHP690.

Optimal rate of convergence for stochastic burgers-type equations

M. Hairer; K. Matetski 

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

M. Hairer 

2016

The Dynamical Sine-Gordon Model

M. Hairer; H. Shen 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2016. Vol. 341, num. 3, p. 933 – 989. DOI : 10.1007/s00220-015-2525-3.

Large scale behaviour of 3D continuous phase coexistence models

M. Hairer; W. Xu 

2016

2015

A Wong-Zakai theorem for stochastic PDEs

M. Hairer; E. Pardoux 

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. 2015. Vol. 67, num. 4, p. 1551 – 1604. DOI : 10.2969/jmsj/06741551.

Regularity structures and the dynamical $Φ^4_3$ model

M. Hairer 

2015

A simple construction of the continuum parabolic Anderson model on R2

M. Hairer; C. Labbe 

ELECTRONIC COMMUNICATIONS IN PROBABILITY. 2015. Vol. 20, p. 1 – 11. DOI : 10.1214/ECP.v20-4038.

Introduction to regularity structures

M. Hairer 

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

M. Hairer; M. Hutzenthaler; A. Jentzen 

ANNALS OF PROBABILITY. 2015. Vol. 43, num. 2, p. 468 – 527. DOI : 10.1214/13-AOP838.

Geometric versus non-geometric rough paths

M. Hairer; D. Kelly 

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

B. Cloez; M. Hairer 

BERNOULLI. 2015. Vol. 21, num. 1, p. 505 – 536. DOI : 10.3150/13-BEJ577.

The Brownian Fan

M. Hairer; J. Weare 

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2015. Vol. 68, num. 1, p. 1 – 60. DOI : 10.1002/cpa.21544.

SMOOTHNESS OF THE DENSITY FOR SOLUTIONS TO GAUSSIAN ROUGH DIFFERENTIAL EQUATIONS

T. Cass; M. Hairer; C. Litterer; S. Tindel 

ANNALS OF PROBABILITY. 2015. Vol. 43, num. 1, p. 188 – 239. DOI : 10.1214/13-AOP896.

2014

SPECTRAL GAPS FOR A METROPOLIS-HASTINGS ALGORITHM IN INFINITE DIMENSIONS

M. Hairer; A. M. Stuart; S. J. Vollmer 

ANNALS OF APPLIED PROBABILITY. 2014. Vol. 24, num. 6, p. 2455 – 2490. DOI : 10.1214/13-AAP982.

Improved Diffusion Monte Carlo

M. Hairer; J. Weare 

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2014. Vol. 67, num. 12, p. 1995 – 2021. DOI : 10.1002/cpa.21526.

A theory of regularity structures

M. Hairer 

INVENTIONES MATHEMATICAE. 2014. Vol. 198, num. 2, p. 269 – 504. DOI : 10.1007/s00222-014-0505-4.

Approximating Rough Stochastic PDEs

M. Hairer; J. Maas; H. Weber 

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2014. Vol. 67, num. 5, p. 776 – 870. DOI : 10.1002/cpa.21495.

Singular stochastic PDEs

M. Hairer 

2014

2013

Random homogenisation of a highly oscillatory singular potential

M. Hairer; E. Pardoux; A. Piatnitski 

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

M. Hairer 

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

M. Hairer; N. S. Pillai 

ANNALS OF PROBABILITY. 2013. Vol. 41, num. 4, p. 2544 – 2598. DOI : 10.1214/12-AOP777.

Rough Burgers-like equations with multiplicative noise

M. Hairer; H. Weber 

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

N. Bou-Rabee; M. Hairer 

IMA JOURNAL OF NUMERICAL ANALYSIS. 2013. Vol. 33, num. 1, p. 80 – 110. DOI : 10.1093/imanum/drs003.

2012

Stochastic PDEs with multiscale structure

M. Hairer; D. Kelly 

ELECTRONIC JOURNAL OF PROBABILITY. 2012. Vol. 17, p. 1 – 38. DOI : 10.1214/EJP.v17-1807.

A SPATIAL VERSION OF THE ITO-STRATONOVICH CORRECTION

M. Hairer; J. Maas 

ANNALS OF PROBABILITY. 2012. Vol. 40, num. 4, p. 1675 – 1714. DOI : 10.1214/11-AOP662.

Triviality of the 2D stochastic Allen-Cahn equation

M. Hairer; M. D. Ryser; H. Weber 

ELECTRONIC JOURNAL OF PROBABILITY. 2012. Vol. 17, p. 1 – 14. DOI : 10.1214/EJP.v17-1731.

Singular perturbations to semilinear stochastic heat equations

M. Hairer 

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

M. Hairer; J. Voss 

JOURNAL OF NONLINEAR SCIENCE. 2011. Vol. 21, num. 6, p. 897 – 920. DOI : 10.1007/s00332-011-9104-3.

Rough Stochastic PDEs

M. Hairer 

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2011. Vol. 64, num. 11, p. 1547 – 1585. DOI : 10.1002/cpa.20383.

On Malliavin’s proof of Hormander’s theorem

M. Hairer 

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

M. Allman; V. Betz; M. Hairer 

STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2011. Vol. 121, num. 9, p. 2014 – 2042. DOI : 10.1016/j.spa.2011.05.007.

Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion

M. Hairer; N. S. Pillai 

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2011. Vol. 47, num. 2, p. 601 – 628. DOI : 10.1214/10-AIHP377.

SAMPLING CONDITIONED HYPOELLIPTIC DIFFUSIONS

M. Hairer; A. M. Stuart; J. Voss 

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

M. Hairer; C. Manson 

ANNALS OF PROBABILITY. 2011. Vol. 39, num. 2, p. 648 – 682. DOI : 10.1214/10-AOP564.

Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations

M. Hairer; J. C. Mattingly; M. Scheutzow 

PROBABILITY THEORY AND RELATED FIELDS. 2011. Vol. 149, num. 1-2, p. 223 – 259. DOI : 10.1007/s00440-009-0250-6.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

M. Hairer; J. C. Mattingly 

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

M. Hairer; C. Manson 

STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2010. Vol. 120, num. 8, p. 1589 – 1605. DOI : 10.1016/j.spa.2010.03.016.

Hypoellipticity in infinite dimensions

M. Hairer 

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

M. Hairer; A. J. Majda 

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?

M. Hairer 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2009. Vol. 292, num. 1, p. 131 – 177. DOI : 10.1007/s00220-009-0857-6.

Stationary distributions for diffusions with inert drift

R. F. Bass; K. Burdzy; Z. Q. Chen; M. Hairer 

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

M. Hairer; J. C. Mattingly 

Communications on Pure and Applied Mathematics. 2009. Vol. 62, num. 8, p. 999 – 1032. DOI : 10.1002/cpa.20280.

An Introduction to Stochastic PDEs

M. Hairer 

2009

Asymptotic coupling and a weak form of Harris’ theorem with applications to stochastic delay equations

M. Hairer; J. C. Mattingly; M. Scheutzow 

2009

Ergodic properties of a class of non-Markovian processes

M. Hairer 

2009

2008

SPECTRAL GAPS IN WASSERSTEIN DISTANCES AND THE 2D STOCHASTIC NAVIER-STOKES EQUATIONS

M. Hairer; J. C. Mattingly 

ANNALS OF PROBABILITY. 2008. Vol. 36, num. 6, p. 2050 – 2091. DOI : 10.1214/08-AOP392.

Homogenization of periodic linear degenerate PDEs

M. Hairer; E. Pardoux 

JOURNAL OF FUNCTIONAL ANALYSIS. 2008. Vol. 255, num. 9, p. 2462 – 2487. DOI : 10.1016/j.jfa.2008.04.014.

Yet another look at Harris’ ergodic theorem for Markov chains

M. Hairer; J. C. Mattingly 

2008

Ornstein-Uhlenbeck processes on Lie groups

F. Baudoin; M. Hairer; J. Teichmann 

JOURNAL OF FUNCTIONAL ANALYSIS. 2008. Vol. 255, num. 4, p. 877 – 890. DOI : 10.1016/j.jfa.2008.05.004.

From Ballistic to diffusive behavior in periodic potentials

M. Hairer; G. A. Pavliotis 

JOURNAL OF STATISTICAL PHYSICS. 2008. Vol. 131, num. 1, p. 175 – 202. DOI : 10.1007/s10955-008-9493-3.

Rigorous remarks about scaling laws in turbulent fluids

F. Flandoli; M. Gubinelli; M. Hairer; M. Romito 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2008. Vol. 278, num. 1, p. 1 – 29. DOI : 10.1007/s00220-007-0398-9.

2007

A version of Hormander’s theorem for the fractional Brownian motion

F. Baudoin; M. Hairer 

PROBABILITY THEORY AND RELATED FIELDS. 2007. Vol. 139, num. 3-4, p. 373 – 395. DOI : 10.1007/s00440-006-0035-0.

Analysis of spdes arising in path sampling part II: The nonlinear case

M. Hairer; A. M. Stuart; J. Voss 

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

M. Hairer; A. Ohashi 

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

D. Bloemker; M. Hairer; G. A. Pavliotis 

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

A. Apte; M. Hairer; A. M. Stuart; J. Voss 

Physica D: Nonlinear Phenomena. 2007. Vol. 230, num. 1-2, p. 50 – 64. DOI : 10.1016/j.physd.2006.06.009.

2006

Multiscale Analysis for SPDEs with Quadratic Nonlinearities

D. Blömker; G. A. Pavliotis; M. Hairer 

2006

Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing

M. Hairer; J. C. Mattingly 

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

D. Blömker; M. Hairer; G. Pavliotis 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2005. Vol. 258, num. 2, p. 479 – 512. DOI : 10.1007/s00220-005-1368-8.

Remarks on the K41 scaling law in turbulent fluids

F. Flandoli; M. Gubinelli; M. Hairer; M. Romito 

2005

A probabilistic argument for the controllability of conservative systems

M. Hairer 

2005

Ergodicity of stochastic differential equations driven by fractional Brownian motion

M. Hairer 

ANNALS OF PROBABILITY. 2005. Vol. 33, num. 2, p. 703 – 758. DOI : 10.1214/009117904000000892.

ANALYSIS OF SPDES ARISING IN PATH SAMPLING PART I: THE GAUSSIAN CASE

M. Hairer; A. M. Stuart; J. Voss; P. Wiberg 

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

M. Hairer; J. Mattingly 

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

M. Hairer; J. Mattingly; É. Pardoux 

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

D. Blomker; M. Hairer 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2004. Vol. 251, num. 3, p. 515 – 555. DOI : 10.1007/s00220-004-1130-7.

Periodic homogenization for hypoelliptic diffusions

M. Hairer; G. A. Pavliotis 

Journal of Statistical Physics. 2004. Vol. 117, num. 1-2, p. 261 – 279. DOI : 10.1023/B:JOSS.0000044055.59822.20.

Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier–Stokes equation

M. Hairer; J. C. Mattingly; E. Pardoux 

2004

Stationary solutions for a model of amorphous thin-film growth

D. Blömker; M. Hairer 

STOCHASTIC ANALYSIS AND APPLICATIONS. 2004. Vol. 22, num. 4, p. 903 – 922. DOI : 10.1081/SAP-120037624.

2003

Spectral properties of hypoelliptic operators

J. Eckmann; M. Hairer 

COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2003. Vol. 235, num. 2, p. 233 – 253. DOI : 10.1007/s00220-003-0805-9.

2002

Exponential mixing properties of stochastic PDEs through asymptotic coupling

M. Hairer 

PROBABILITY THEORY AND RELATED FIELDS. 2002. Vol. 124, num. 3, p. 345 – 380. DOI : 10.1007/s004400200216.

Exponential mixing for a stochastic partial differential equation driven by degenerate noise

M. Hairer 

Nonlinearity. 2002. Vol. 15, num. 2, p. 271 – 279. DOI : 10.1088/0951-7715/15/2/304.

2001

Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise

J. P. Eckmann; M. Hairer 

Communications in Mathematical Physics. 2001. Vol. 219, num. 3, p. 523 – 565. DOI : 10.1007/s002200100424.

Invariant measures for stochastic partial differential equations in unbounded domains

J. P. Eckmann; M. Hairer 

Nonlinearity. 2001. Vol. 14, num. 1, p. 133 – 151. DOI : 10.1088/0951-7715/14/1/308.

2000

Non-equilibrium statistical mechanics of strongly anharmonic chains of oscillators

J. P. Eckmann; M. Hairer 

Communications in Mathematical Physics. 2000. Vol. 212, num. 1, p. 105 – 164. DOI : 10.1007/s002200000216.