# Martin Hairer

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Austrian-British mathematician working in stochastic analysis

## Martin Hairer's AcademicInfluence.com Rankings

Martin Hairermathematics Degrees

Mathematics

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#1271

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Statistics

#393

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#461

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Measure Theory

#1186

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#1512

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Mathematics

## Martin Hairer's Degrees

- Masters Mathematics University of Geneva
- Bachelors Mathematics University of Geneva

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## Why Is Martin Hairer Influential?

(Suggest an Edit or Addition)According to Wikipedia, Sir Martin Hairer is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL and at Imperial College London. He previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.

## Martin Hairer's Published Works

### Published Works

- A theory of regularity structures (2013) (839)
- Solving the KPZ equation (2011) (581)
- Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing (2004) (515)
- A Course on Rough Paths (2020) (369)
- Yet Another Look at Harris’ Ergodic Theorem for Markov Chains (2008) (321)
- A Course on Rough Paths: With an Introduction to Regularity Structures (2014) (292)
- Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations (2009) (238)
- An Introduction to Stochastic PDEs (2009) (221)
- Algebraic renormalisation of regularity structures (2016) (188)
- Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations (2006) (179)
- A Wong-Zakai theorem for stochastic PDEs (2014) (179)
- Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions (2011) (163)
- Non-Equilibrium Statistical Mechanics¶of Strongly Anharmonic Chains of Oscillators (1999) (152)
- Exponential mixing properties of stochastic PDEs through asymptotic coupling (2001) (149)
- An analytic BPHZ theorem for regularity structures (2016) (144)
- A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs (2008) (139)
- Exponential ergodicity for Markov processes with random switching (2013) (138)
- A CLASS OF GROWTH MODELS RESCALING TO KPZ (2015) (136)
- Sampling the posterior: An approach to non-Gaussian data assimilation (2007) (135)
- ANALYSIS OF SPDES ARISING IN PATH SAMPLING PART II: THE NONLINEAR CASE (2006) (129)
- A simple framework to justify linear response theory (2009) (126)
- Multiplicative stochastic heat equations on the whole space (2015) (119)
- On Malliavinʼs proof of Hörmanderʼs theorem (2011) (118)
- Introduction to regularity structures (2014) (117)
- Ergodicity of stochastic differential equations driven by fractional Brownian motion (2003) (114)
- Uniqueness of the Invariant Measure¶for a Stochastic PDE Driven by Degenerate Noise (2000) (114)
- Spectral Properties of Hypoelliptic Operators (2002) (113)
- Renormalising SPDEs in regularity structures (2017) (95)
- A version of Hörmander’s theorem for the fractional Brownian motion (2007) (95)
- Analysis of SPDEs arising in path sampling. Part I: The Gaussian case (2005) (93)
- Non-asymptotic mixing of the MALA algorithm (2010) (89)
- Loss of regularity for Kolmogorov equations (2012) (87)
- Geometric versus non-geometric rough paths (2012) (84)
- The Dynamical Sine-Gordon Model (2014) (84)
- A simple construction of the continuum parabolic Anderson model on R 2 (2015) (82)
- A central limit theorem for the KPZ equation (2015) (82)
- Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions (2014) (81)
- Smoothness of the density for solutions to Gaussian rough differential equations (2012) (81)
- Rough stochastic PDEs (2010) (80)
- Discretisations of rough stochastic PDEs (2015) (80)
- The strong Feller property for singular stochastic PDEs (2016) (76)
- Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths (2011) (73)
- Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion (2009) (71)
- Slow energy dissipation in anharmonic oscillator chains (2007) (66)
- Triviality of the 2D stochastic Allen-Cahn equation (2012) (64)
- Periodic Homogenization for Hypoelliptic Diffusions (2004) (61)
- Rough Burgers-like equations with multiplicative noise (2010) (58)
- From Ballistic to Diffusive Behavior in Periodic Potentials (2007) (58)
- Ergodic theory for SDEs with extrinsic memory (2006) (58)
- Approximations to the Stochastic Burgers Equation (2010) (55)
- Averaging dynamics driven by fractional Brownian motion (2019) (49)
- The motion of a random string (2016) (46)
- A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$ (2015) (45)
- Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities (2007) (42)
- Modulation Equations: Stochastic Bifurcation in Large Domains (2004) (41)
- Approximating Rough Stochastic PDEs (2012) (41)
- Singular SPDEs in domains with boundaries (2017) (40)
- Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods (2011) (39)
- Geometric stochastic heat equations (2019) (39)
- The reconstruction theorem in Besov spaces (2016) (39)
- How Hot Can a Heat Bath Get? (2008) (38)
- Multiscale Expansion of Invariant Measures for SPDEs (2004) (38)
- Regularity structures and the dynamical Φ 43 model (2015) (37)
- The dynamical sine-Gordon model in the full subcritical regime (2018) (36)
- Random homogenisation of a highly oscillatory singular potential (2013) (36)
- Singular stochastic PDEs (2014) (35)
- Homogenization of periodic linear degenerate PDEs (2007) (33)
- A Solution Theory for Quasilinear Singular SPDEs (2017) (32)
- GniCodes - Matlab programs for geometric numerical integration (2003) (31)
- Invariant Measures for Stochastic PDE's in Unbounded Domains (2000) (31)
- Langevin dynamic for the 2D Yang–Mills measure (2020) (30)
- Rigorous Remarks about Scaling Laws in Turbulent Fluids (2008) (28)
- Ergodic properties of a class of non-Markovian processes (2007) (27)
- Sampling conditioned diffusions (2009) (26)
- Non-equilibrium steady states for networks of oscillators (2017) (26)
- An analyst's take on the BPHZ theorem (2016) (26)
- Ornstein-Uhlenbeck processes on Lie groups (2007) (25)
- Discretisation of regularity structures (2017) (25)
- Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations (2004) (24)
- A spatial version of the Itô–Stratonovich correction (2010) (24)
- A fractional kinetic process describing the intermediate time behaviour of cellular flows (2016) (24)
- Large scale limit of interface fluctuation models (2018) (23)
- Improved Diffusion Monte Carlo (2012) (20)
- Sampling conditioned hypoelliptic diffusions (2009) (20)
- Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures (2005) (20)
- Stationary distributions for diffusions with inert drift (2008) (20)
- Hörmander’s theorem for semilinear SPDEs (2018) (19)
- Large‐Scale Behavior of Three‐Dimensional Continuous Phase Coexistence Models (2018) (19)
- Ergodic theory for Stochastic PDEs (2008) (18)
- Stochastic quantisation of Yang-Mills-Higgs in 3D (2022) (18)
- Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations (2004) (18)
- Large scale behaviour of 3D continuous phase coexistence models (2016) (17)
- Singular perturbations to semilinear stochastic heat equations (2010) (16)
- Fluctuations Around a Homogenised Semilinear Random PDE (2019) (16)
- Periodic homogenization with an interface: The multi-dimensional case (2009) (15)
- Ergodic Properties of Markov Processes (2006) (15)
- Stationary Solutions for a Model of Amorphous Thin-Film Growth (2002) (14)
- The support of singular stochastic PDEs (2019) (14)
- A version of H¨ ormander's theorem for the fractional (2006) (14)
- Large scale behaviour of 3D phase coexistence models (2016) (14)
- A Bayesian Approach to Data Assimilation (2005) (14)
- Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization (2016) (13)
- Exponential mixing for a stochastic partial differential equation driven by degenerate noise (2001) (13)
- STOCHASTIC SWIFT-HOHENBERG EQUATION NEAR A CHANGE OF STABILITY (2005) (13)
- Regularity structures and the dynamical $\Phi^4_3$ model (2015) (13)
- Convergence of Markov Processes August (2010) (13)
- From averaging to homogenization in cellular flows - an exact description of the transition (2014) (12)
- Renormalisation of Stochastic Partial Differential Equations (2020) (12)
- Optimal rate of convergence for stochastic Burgers-type equations (2015) (12)
- Renormalisation of parabolic stochastic PDEs (2018) (11)
- A probabilistic argument for the controllability of conservative systems (2005) (10)
- COUPLING STOCHASTIC PDES (2006) (10)
- A Noise-Induced Transition in the Lorenz System (2020) (9)
- Hypoellipticity in Infinite Dimensions (2009) (7)
- The support of singular stochastic partial differential equations (2022) (7)
- Periodic homogenization with an interface: The one-dimensional case (2009) (7)
- Tightness of the Ising–Kac Model on the Two-Dimensional Torus (2017) (7)
- Advanced stochastic analysis (2016) (7)
- A chain of interacting particles under strain (2010) (6)
- The Asian Mathematical Conference 2016 (AMC 2016) (2017) (6)
- Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds (2012) (5)
- Multiscale Analysis for SPDEs with Quadratic Nonlinearities (2006) (5)
- The BPHZ Theorem for Regularity Structures via the Spectral Gap Inequality (2023) (4)
- A scaling limit of the parabolic Anderson model with exclusion interaction (2021) (4)
- The Allen–Cahn equation with generic initial datum (2022) (4)
- The Brownian Castle (2020) (4)
- The 8 43 Measure Has Sub-Gaussian Tails (2022) (4)
- Some Remarks on Stabilization by Additive Noise (2008) (4)
- The Brownian Fan (2014) (3)
- Generating Diffusions with Fractional Brownian Motion (2021) (3)
- Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation (2004) (3)
- Boundary renormalisation of SPDEs (2021) (2)
- Periodic homogenization with an interface (2009) (2)
- Remarks on the K41 scaling law in turbulent fluids (2005) (2)
- Directed mean curvature flow in noisy environment (2022) (2)
- Exponential Mixing Properties of Stochastic PDEs (2001) (2)
- Convergence of Markov Processes January 13 , 2016 (2016) (2)
- Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise (2023) (1)
- ON MARTIN HAIRER’S THEORY OF REGULARITY STRUCTURES (2015) (1)
- Introduction to Hypoelliptic Schrödinger type operators (2007) (1)
- Slow energy dissipation in chains of anharmonic oscillators December 11 , 2007 (2007) (1)
- N ov 2 01 7 Singular SPDEs in domains with boundaries November 10 , 2017 (2017) (1)
- The $$\Phi _3^4$$ Measure Has Sub-Gaussian Tails (2021) (1)
- Erratum to: Rough Burgers-like equations with multiplicative noise (2013) (1)
- Stochastic PDEs with multiscale structure (2012) (1)
- Stochastic integration and Itô’s formula (2019) (1)
- On the controllability of conservative systems (2005) (1)
- Improved diffusion Monte Carlo and the Brownian fan (2012) (1)
- Algebraic renormalisation of regularity structures (2018) (0)
- 0 50 60 64 v 1 2 4 Ju n 20 05 On the controllability of conservative systems (2005) (0)
- P R ] 27 M ar 2 01 3 Exponential ergodicity for Markov processes with random switching February 7 , 2014 (2014) (0)
- Operations on modelled distributions (2020) (0)
- A pr 2 01 5 Multiplicative stochastic heat equations on the whole space April 28 , 2015 (2015) (0)
- Singular perturbations to semilinear stochastic heat equations (2010) (0)
- A P ] 4 F eb 2 01 8 Renormalising SPDEs in regularity structures (0)
- Gaussian rough paths (2020) (0)
- S ep 2 01 0 Singular perturbations to semilinear stochastic heat equations September 21 , 2010 (2010) (0)
- The reconstruction theorem in Besov spaces September 16 , 2016 (2016) (0)
- Introduction (2020) (0)
- Ergodic theory for SDEs with extrinsic memory April (2008) (0)
- J an 2 01 2 Triviality of the 2 D stochastic (2013) (0)
- P R ] 18 S ep 2 00 1 Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling September 14 , 2001 (2022) (0)
- Fluctuations of stochastic PDEs with long-range correlations (2023) (0)
- Fluctuations Around a Homogenised Semilinear Random PDE (2020) (0)
- Multiscale Analysis for SPDEs with Quadratic Nonlinearities November 28 , 2006 (2006) (0)
- A central limit theorem for the KPZ equation July 5 , 2015 (2015) (0)
- 0 40 30 03 v 1 3 M ar 2 00 4 Periodic Homogenization for Hypoelliptic Diffusions (2004) (0)
- PR ] 8 A ug 2 01 8 The dynamical sine-Gordon model in the full subcritical regime August 9 , 2018 (2018) (0)
- A theory of regularity structures (2014) (0)
- Optimal rate of convergence for stochastic Burgers-type equations (2015) (0)
- Stochastic Analysis: Around the KPZ Universality Class (2014) (0)
- Random homogenisation of a highly oscillatory singular potential (2013) (0)
- Modulation Equations : Stochastic Bifurcation in Large Domains November 23 , 2004 (2004) (0)
- A Fields Medal for (2015) (0)
- Preface Since its original development in the mid-nineties by Terry Lyons , culminating in the landmark paper (2015) (0)
- 0 20 40 44 v 1 2 3 A pr 2 00 2 Stationary solutions for a model of amorphous thin-film growth October 25 , 2018 (2018) (0)
- October 2014 Cover English (2014) (0)
- Erratum to: Rough Burgers-like equations with multiplicative noise (2013) (0)
- The reconstruction theorem in Besov spaces August 25 , 2018 (2018) (0)
- Stochastic partial differential equations (2020) (0)
- The work of Hugo Duminil-Copin (2022) (0)
- Rough Burgers-like equations with multiplicative noise (2011) (0)
- Introduction to Regularity Structures August 29 , 2013 (2013) (0)
- Application to the KPZ equation (2020) (0)
- The dynamical sine-Gordon model September 18 , 2014 (2014) (0)
- PR ] 2 8 O ct 2 02 2 The Φ 43 measure has sub-Gaussian tails October 31 , 2022 (2022) (0)
- N ov 2 00 6 Multiscale Analysis for SPDEs with Quadratic Nonlinearities May 14 (2019) (0)
- Stochastic differential equations (2020) (0)
- The motion of a random string August 10 , 2016 (2016) (0)
- A P ] 2 9 M ar 2 01 8 Multiplicative stochastic heat equations on the whole space September 30 , 2018 (2018) (0)
- The Dynamical Sine-Gordon Model (2015) (0)
- Stochastic Modulation Equations (2005) (0)
- Corrigendum: Improved Diffusion Monte Carlo (2015) (0)
- Introduction to Regularity Structures March 27 , 2014 (2014) (0)
- The space of rough paths (2020) (0)
- 0 Ju l 2 00 2 Spectral Properties of Hypoelliptic Operators (0)
- 15 S ep 2 00 0 Uniqueness of the Invariant Measure for a Stochastic PDE Driven by Degenerate Noise February 8 , 2008 (2008) (0)
- Singular perturbations to semilinear stochastic heat equations April 1 , 2010 (2010) (0)
- Ju l 2 01 7 Discretisations of rough stochastic PDEs September 30 , 2018 (0)
- Renormalisation of parabolic stochastic PDEs (2018) (0)
- PR ] 1 2 A pr 2 00 8 Stationary distributions for diffusions with inert drift ∗ (2021) (0)
- A fresh look on the Phi^4 model (2019) (0)
- Cameron–Martin regularity and applications (2020) (0)
- Large-scale limit of interface fluctuation models February 23 , 2018 (2018) (0)
- Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion (2009) (0)
- An Introduction to Stochastic PDEs January 26 , 2009 (2009) (0)
- ERGODIC THEORY FOR SDEs WITH EXTRINSIC MEMORY1 (2007) (0)
- N ov 2 01 7 Singular SPDEs in domains with boundaries March 11 , 2022 (2022) (0)
- Integration against rough paths (2020) (0)
- The Brownian Web as a random $\mathbb R$-tree (2021) (0)
- A COURSE ON INTEGRATION BY PARTS (2022) (0)
- 0 50 70 44 v 1 1 8 Ju l 2 00 5 Remarks on the K 41 scaling law in turbulent fluids (2005) (0)
- Stochastic Analysis: Geometry of Random Processes (2018) (0)
- Large-scale limit of interface fluctuation models August 27 , 2018 (2018) (0)
- Averaging dynamics driven by fractional Brownian motion February 28 , 2019 (2019) (0)
- Advanced functional analysis (2015) (0)
- Rédacteurs en chef / Chief Editors (2014) (0)
- Discretisations of rough stochastic PDEs December (2015) (0)
- Periodic Homogenization for Hypoelliptic Diffusions March (2004) (0)
- Multiscale expansion of invariant measures for SPDEs September 30 , 2003 (2003) (0)
- A ug 2 01 5 Regularity structures and the dynamical Φ 43 model August 24 , 2015 (2015) (0)
- S ep 2 01 4 The dynamical sine-Gordon model (2014) (0)
- J un 2 01 6 The motion of a random string June 22 (2016) (0)
- M ar 2 01 1 On Malliavin ’ s proof of H örmander ’ s theorem January 14 (2013) (0)
- Brownian motion as a rough path (2020) (0)
- E LEMENTS OF P ROBABILITY THEORY 2 2 Elements of Probability theory (2006) (0)
- Introduction (2019) (0)
- PAM R2 (2015) (0)
- A pr 2 00 3 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 20 , 2008 (2003) (0)
- O ct 2 01 6 A central limit theorem for the KPZ equation October (2016) (0)
- N ov 2 01 7 Singular SPDEs in domains with boundaries July 23 , 2020 (2020) (0)
- A ug 2 00 9 Sampling Conditioned Hypoelliptic Diffusions (2009) (0)
- Operations on controlled rough paths (2020) (0)
- N ov 2 01 7 Singular SPDEs in domains with boundaries September 1 , 2018 (2018) (0)
- Tightness of the Ising–Kac Model on the Two-Dimensional Torus (2018) (0)
- 0 20 40 44 v 1 2 3 A pr 2 00 2 Stationary solutions for a model of amorphous thin-film growth February 7 , 2008 (2002) (0)
- Ja n 20 06 Analysis of SPDEs Arising in Path Sampling Part II : The Nonlinear Case February 27 , 2008 (0)
- Solutions to rough differential equations (2020) (0)
- ar 2 00 4 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 1 , 2008 (2003) (0)
- Singular SPDEs in domains with boundaries (2018) (0)
- Convergence of Markov Processes (2021) (0)
- Communications in Mathematical Physics Modulation Equations : Stochastic Bifurcation in Large Domains (2005) (0)
- ormander's theorem for the fractional Brownian motion (2008) (0)
- Doob–Meyer type decomposition for rough paths (2014) (0)

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## What Schools Are Affiliated With Martin Hairer?

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