#16,543

Most Influential Person

Austrian-British mathematician working in stochastic analysis

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Sir Martin Hairer is currently a professor of mathematics and Chair in Probability and Stochastic Analysis at Imperial College London in the Faculty of Natural Sciences, Department of Mathematics. Previously, he held roles at the University of Warwick, and the Courant Institute of New York University. An Austrian Citizen born in Geneva, Switzerland, Hairer completed his BS in mathematics at the University of Geneva in 1994. He stayed there for his MS and PhD in physics, completed in 2001.

Hairer is known as the leading name in stochastic partial differential equations, with significant implications for areas including quantum field theory and spatial modeling. In his research, Hairer has produced groundbreaking results in the construction of stochastic systems, stochastic analysis techniques, and his theory of regularity structures, fueling further research and advancement.

For his work, Hairer has received awards and honors including the 2014 Fields Medal, the Whitehead Prize, an Advanced Research Fellowship with the Engineering and Physical Sciences Research Council, Fellowship with the Royal Society, and holds the honorary title of Knight Commander of the Order of the British Empire.

**Featured in Top Influential Mathematicians Today**

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 Imperial College London, having 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.

- A theory of regularity structures (2014) (640)
- Solving the KPZ equation (2011) (466)
- Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing (2004) (426)
- A Course on Rough Paths (2014) (361)
- Yet Another Look at Harris’ Ergodic Theorem for Markov Chains (2011) (257)
- A Course on Rough Paths: With an Introduction to Regularity Structures (2014) (229)
- Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations (2009) (182)
- An Introduction to Stochastic PDEs (2009) (182)
- Algebraic renormalisation of regularity structures (2018) (150)
- Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations (2008) (146)
- Non-Equilibrium Statistical Mechanics¶of Strongly Anharmonic Chains of Oscillators (1999) (138)
- A Wong-Zakai theorem for stochastic PDEs (2014) (134)
- Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions (2014) (133)
- Exponential mixing properties of stochastic PDEs through asymptotic coupling (2001) (129)
- Sampling the posterior: An approach to non-Gaussian data assimilation (2007) (122)
- ANALYSIS OF SPDES ARISING IN PATH SAMPLING PART II: THE NONLINEAR CASE (2007) (115)
- An analytic BPHZ theorem for regularity structures (2016) (114)
- A CLASS OF GROWTH MODELS RESCALING TO KPZ (2018) (113)
- Exponential ergodicity for Markov processes with random switching (2013) (110)
- A simple framework to justify linear response theory (2010) (108)
- A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs (2008) (107)
- On Malliavinʼs proof of Hörmanderʼs theorem (2011) (104)
- Spectral Properties of Hypoelliptic Operators (2002) (101)
- Uniqueness of the Invariant Measure¶for a Stochastic PDE Driven by Degenerate Noise (2001) (100)
- Ergodicity of stochastic differential equations driven by fractional Brownian motion (2003) (97)
- Introduction to Regularity Structures (2014) (95)
- Multiplicative stochastic heat equations on the whole space (2015) (95)
- A version of Hörmander’s theorem for the fractional Brownian motion (2007) (84)
- Analysis of SPDEs arising in path sampling. Part I: The Gaussian case (2005) (80)
- Loss of regularity for Kolmogorov equations (2015) (74)
- Non-asymptotic mixing of the MALA algorithm (2010) (74)
- Rough Stochastic PDEs (2010) (73)
- Renormalising SPDEs in regularity structures (2017) (72)
- Geometric versus non-geometric rough paths (2012) (70)
- A central limit theorem for the KPZ equation (2015) (69)
- Smoothness of the density for solutions to Gaussian rough differential equations (2015) (65)
- Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths (2013) (64)
- Discretisations of rough stochastic PDEs (2015) (63)
- The Dynamical Sine-Gordon Model (2014) (62)
- Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions (2015) (62)
- Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion (2009) (60)
- Slow energy dissipation in anharmonic oscillator chains (2007) (58)
- Triviality of the 2D stochastic Allen-Cahn equation (2012) (55)
- From Ballistic to Diffusive Behavior in Periodic Potentials (2008) (54)
- Periodic Homogenization for Hypoelliptic Diffusions (2004) (54)
- The strong Feller property for singular stochastic PDEs (2018) (53)
- Ergodic theory for SDEs with extrinsic memory (2007) (51)
- Rough Burgers-like equations with multiplicative noise (2013) (50)
- Approximations to the Stochastic Burgers Equation (2011) (46)
- A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$ (2015) (46)
- Convergence of Markov Processes August (2010) (40)
- The motion of a random string (2016) (38)
- Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods (2011) (36)
- Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities (2007) (34)
- Approximating rough stochastic PDEs (2012) (32)
- Multiscale Expansion of Invariant Measures for SPDEs (2004) (32)
- How Hot Can a Heat Bath Get? (2009) (31)
- Random homogenisation of a highly oscillatory singular potential (2013) (31)
- Averaging dynamics driven by fractional Brownian motion (2019) (31)
- The reconstruction theorem in Besov spaces (2017) (30)
- Invariant Measures for Stochastic PDE's in Unbounded Domains (2000) (29)
- Homogenization of periodic linear degenerate PDEs (2008) (28)
- A Solution Theory for Quasilinear Singular SPDEs (2019) (28)
- Singular stochastic PDEs (2014) (28)
- GniCodes - Matlab programs for geometric numerical integration (2003) (28)
- Singular SPDEs in domains with boundaries (2017) (27)
- Regularity structures and the dynamical Φ 43 model (2015) (26)
- Geometric stochastic heat equations (2019) (25)
- Ergodic Properties of Markov Processes (2006) (24)
- Sampling conditioned diffusions (2009) (24)
- Rigorous Remarks about Scaling Laws in Turbulent Fluids (2008) (24)
- Ergodic properties of a class of non-Markovian processes (2009) (23)
- An analyst's take on the BPHZ theorem (2016) (22)
- Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations (2004) (22)
- Non-equilibrium steady states for networks of oscillators (2018) (22)
- Ornstein-Uhlenbeck processes on Lie groups (2007) (21)
- A spatial version of the Itô–Stratonovich correction (2012) (20)
- Discretisation of regularity structures (2019) (19)
- Sampling conditioned hypoelliptic diffusions (2009) (18)
- A fractional kinetic process describing the intermediate time behaviour of cellular flows (2016) (18)
- Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations (2004) (17)
- Stationary distributions for diffusions with inert drift (2008) (17)
- Ergodic theory for Stochastic PDEs (2008) (17)
- Improved diffusion Monte Carlo (2012) (17)
- Large scale limit of interface fluctuation models (2019) (16)
- Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures (2005) (15)
- Hörmander’s theorem for semilinear SPDEs (2019) (15)
- Large scale behaviour of 3D continuous phase coexistence models (2016) (14)
- A version of H¨ ormander's theorem for the fractional (2006) (14)
- A Bayesian Approach to Data Assimilation (2005) (13)
- Regularity structures and the dynamical $\Phi^4_3$ model (2014) (13)
- Singular perturbations to semilinear stochastic heat equations (2010) (13)
- Large‐Scale Behavior of Three‐Dimensional Continuous Phase Coexistence Models (2018) (13)
- Stationary Solutions for a Model of Amorphous Thin-Film Growth (2002) (13)
- Exponential mixing for a stochastic partial differential equation driven by degenerate noise (2002) (12)
- Large scale behaviour of 3D phase coexistence models (2016) (12)
- Langevin dynamic for the 2D Yang-Mills measure (2020) (11)
- Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization (2018) (11)
- From averaging to homogenization in cellular flows - an exact description of the transition (2014) (10)
- A probabilistic argument for the controllability of conservative systems (2005) (10)
- Periodic homogenization with an interface: The multi-dimensional case (2011) (9)
- STOCHASTIC SWIFT-HOHENBERG EQUATION NEAR A CHANGE OF STABILITY (2005) (9)
- Optimal rate of convergence for stochastic Burgers-type equations (2015) (9)
- The support of singular stochastic PDEs (2019) (8)
- COUPLING STOCHASTIC PDES (2006) (8)
- Renormalisation of parabolic stochastic PDEs (2018) (8)
- Fluctuations Around a Homogenised Semilinear Random PDE (2021) (8)
- A chain of interacting particles under strain (2010) (6)
- Renormalisation of Stochastic Partial Differential Equations (2020) (6)
- Tightness of the Ising–Kac Model on the Two-Dimensional Torus (2017) (6)
- Periodic homogenization with an interface: The one-dimensional case (2010) (5)
- Some Remarks on Stabilization by Additive Noise (2008) (4)
- Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds (2012) (4)
- Hypoellipticity in Infinite Dimensions (2009) (4)
- A Course on Rough Paths (2020) (4)
- The Brownian Fan (2014) (3)
- Convergence of Markov Processes January 13 , 2016 (2016) (3)
- Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation (2004) (3)
- A Noise-Induced Transition in the Lorenz System (2020) (3)
- Periodic homogenization with an interface (2009) (2)
- Exponential Mixing Properties of Stochastic PDEs (2001) (2)
- Remarks on the K41 scaling law in turbulent fluids (2005) (2)
- Advanced stochastic analysis (2016) (2)
- Erratum to: Rough Burgers-like equations with multiplicative noise (2013) (1)
- Stochastic quantisation of Yang-Mills-Higgs in 3D (2022) (1)
- Stochastic integration and Ito's formula (2014) (1)
- Generating diffusions with fractional Brownian motion (2021) (1)
- 0 40 30 03 v 1 3 M ar 2 00 4 Periodic Homogenization for Hypoelliptic Diffusions (2004) (1)
- Large-scale limit of interface fluctuation models August 27 , 2018 (2018) (1)
- The support of singular stochastic partial differential equations (2022) (1)
- N ov 2 01 7 Singular SPDEs in domains with boundaries November 10 , 2017 (2017) (1)
- ON MARTIN HAIRER’S THEORY OF REGULARITY STRUCTURES (2015) (1)
- Modulation Equations : Stochastic Bifurcation in Large Domains November 23 , 2004 (2004) (1)
- On the controllability of conservative systems (2005) (1)
- Directed mean curvature flow in noisy environment (2022) (1)
- The Brownian Castle (2020) (1)
- Improved diffusion Monte Carlo and the Brownian fan (2012) (1)
- Introduction to Hypoelliptic Schrödinger type operators (2007) (1)
- Slow energy dissipation in chains of anharmonic oscillators December 11 , 2007 (2007) (1)
- An Introduction to Stochastic PDEs January 26 , 2009 (2009) (1)
- Ja n 20 06 Analysis of SPDEs Arising in Path Sampling Part II : The Nonlinear Case February 27 , 2008 (0)
- Application to the KPZ equation (2020) (0)
- Solutions to rough differential equations (2014) (0)
- Stochastic integration and Itô’s formula (2020) (0)
- PR ] 1 2 A pr 2 00 8 Stationary distributions for diffusions with inert drift ∗ (2021) (0)
- A Fields Medal for (2015) (0)
- The Brownian Web as a random $\mathbb R$-tree (2021) (0)
- Stochastic Partial Differential Equations (2014) (0)
- Solutions to rough differential equations (2020) (0)
- Introduction to Regularity Structures August 29 , 2013 (2013) (0)
- Gaussian rough paths (2020) (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)
- Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion (2009) (0)
- Stochastic Modulation Equations (2005) (0)
- October 2014 Cover English (2014) (0)
- Introduction to regularity structures (2020) (0)
- Ergodic theory for SDEs with extrinsic memory April (2008) (0)
- Convergence of Markov Processes (2021) (0)
- ERGODIC THEORY FOR SDEs WITH EXTRINSIC MEMORY1 (2007) (0)
- A ug 2 00 9 Sampling Conditioned Hypoelliptic Diffusions (2009) (0)
- Gaussian rough paths (2014) (0)
- Doob–Meyer type decomposition for rough paths (2014) (0)
- The Allen-Cahn equation with generic initial datum (2022) (0)
- Integration against rough paths (2014) (0)
- Ju l 2 01 7 Discretisations of rough stochastic PDEs September 30 , 2018 (0)
- The space of rough paths (2014) (0)
- Introduction (2019) (0)
- Singular perturbations to semilinear stochastic heat equations April 1 , 2010 (2010) (0)
- Cameron–Martin Regularity and Applications (2014) (0)
- 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)
- The motion of a random string August 10 , 2016 (2016) (0)
- 0 Ju l 2 00 2 Spectral Properties of Hypoelliptic Operators (0)
- A P ] 2 9 M ar 2 01 8 Multiplicative stochastic heat equations on the whole space September 30 , 2018 (2018) (0)
- N ov 2 01 7 Singular SPDEs in domains with boundaries July 23 , 2020 (2020) (0)
- Stochastic PDEs with multiscale structure (2012) (0)
- Cameron–Martin regularity and applications (2020) (0)
- 0 50 60 64 v 1 2 4 Ju n 20 05 On the controllability of conservative systems (2005) (0)
- A fresh look on the Phi^4 model (2019) (0)
- A scaling limit of the parabolic Anderson model with exclusion interaction (2016) (0)
- The reconstruction theorem in Besov spaces August 25 , 2018 (2018) (0)
- Operations on modelled distributions (2020) (0)
- A central limit theorem for the KPZ equation July 5 , 2015 (2015) (0)
- Boundary renormalisation of SPDEs (2021) (0)
- Multiscale expansion of invariant measures for SPDEs September 30 , 2003 (2003) (0)
- Introduction (2020) (0)
- Corrigendum: Improved Diffusion Monte Carlo (2015) (0)
- Discretisations of rough stochastic PDEs December (2015) (0)
- Rédacteurs en chef / Chief Editors (2014) (0)
- E LEMENTS OF P ROBABILITY THEORY 2 2 Elements of Probability theory (2006) (0)
- Operations on controlled rough paths (2014) (0)
- Multiscale Analysis for SPDEs with Quadratic Nonlinearities November 28 , 2006 (2006) (0)
- Stochastic partial differential equations (2020) (0)
- A pr 2 00 3 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 20 , 2008 (2003) (0)
- Advanced functional analysis (2015) (0)
- The reconstruction theorem in Besov spaces September 16 , 2016 (2016) (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)
- The dynamical sine-Gordon model September 18 , 2014 (2014) (0)
- Stochastic differential equations (2020) (0)
- Preface Since its original development in the mid-nineties by Terry Lyons , culminating in the landmark paper (2015) (0)
- Stochastic differential equations (2014) (0)
- ar 2 00 4 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 1 , 2008 (2003) (0)
- Let B be standard d-dimensional Brownian motion and v a bounded measurable vector field on ∂ (0)
- Large-scale limit of interface fluctuation models February 23 , 2018 (2018) (0)
- A P ] 4 F eb 2 01 8 Renormalising SPDEs in regularity structures (0)
- The $$\Phi _3^4$$ Measure Has Sub-Gaussian Tails (2022) (0)
- Periodic Homogenization for Hypoelliptic Diffusions March (2004) (0)
- Application to the KPZ Equation (2014) (0)
- The space of rough paths (2020) (0)
- Brownian motion as a rough path (2020) (0)
- Integration against rough paths (2020) (0)
- Introduction to Regularity Structures March 27 , 2014 (2014) (0)
- Operations on controlled rough paths (2020) (0)
- Averaging dynamics driven by fractional Brownian motion February 28 , 2019 (2019) (0)
- 0 A ug 2 00 4 Modulation Equations : Stochastic Bifurcation in Large Domains February 7 , 2008 (2008) (0)
- N ov 2 00 6 Multiscale Analysis for SPDEs with Quadratic Nonlinearities May 14 (2019) (0)
- PR ] 8 A ug 2 01 8 The dynamical sine-Gordon model in the full subcritical regime August 9 , 2018 (2018) (0)
- N ov 2 01 7 Singular SPDEs in domains with boundaries September 1 , 2018 (2018) (0)
- N ov 2 00 6 Multiscale Analysis for SPDEs with Quadratic Nonlinearities February 2 , 2008 (2008) (0)
- Stochastic Analysis: Around the KPZ Universality Class (2014) (0)
- ormander's theorem for the fractional Brownian motion (2008) (0)
- Operations on Modelled Distributions (2014) (0)
- Brownian motion as a rough path (2014) (0)
- S ep 2 01 4 The dynamical sine-Gordon model (2014) (0)
- Communications in Mathematical Physics Modulation Equations : Stochastic Bifurcation in Large Domains (2005) (0)

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