#11,416

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

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