Hairer, Martin

1. An Introduction to Stochastic PDEs
   2009/07/23 by Martin Hairer, Hairer, Martin · 26 citations
   Economics, Econometrics and Finance · Computer Science · Mathematics · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations
2. Solving the KPZ equation
   2011/09/30 by Martin Hairer, Hairer, Martin · 13 citations
   Computer Science · #35Q82 #60H15 #60K35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Polynomial and algebraic computation #Probability (math.PR)
3. Yet another look at Harris' ergodic theorem for Markov chains
   2008/10/15 by Martin Hairer, Jonathan C. Mattingly, Hairer, Martin +1 · 11 citations
   Mathematics · Computer Science · #Markov Chains and Monte Carlo Methods #Advanced Graph Theory Research #Complexity and Algorithms in Graphs
4. Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations
   2009/02/26 by Hairer, Martin, Mattingly, Jonathan C., Scheutzow, Michael · 11 citations
   #34K50 #37A25 #37A30 #37L55 #60H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
5. Algebraic renormalisation of regularity structures
   2016/10/26 by Yvain Bruned, Bruned, Yvain, Martin Hairer +3 · 15 citations
   Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Rings and Algebras (math.RA)
6. Geometric versus non-geometric rough paths
   2012/10/23 by Hairer, Martin, Kelly, David · 8 citations
   #16T05 #34K28 #60H10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)
7. An analytic BPHZ theorem for regularity structures
   2016/12/24 by Ajay Chandra, Chandra, Ajay, Martin Hairer +1 · 10 citations
   Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Risk and Portfolio Optimization
8. A class of growth models rescaling to KPZ
   2015/12/24 by Hairer, Martin, Quastel, Jeremy · 5 citations
   #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
9. A Theory of Hypoellipticity and Unique Ergodicity for Semilinear\n Stochastic PDEs
   2008/08/09 by Martin Hairer, Jonathan C. Mattingly, Hairer, Martin +1 · 4 citations
   Computer Science · Economics, Econometrics and Finance · Mathematics · #35J60 #35R60 #37A25 #37A60 #37L55 #37N10 #60H07 #60H15 #60H30 #76B03 #76F20 #76F55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications
10. The strong Feller property for singular stochastic PDEs
    2016/10/11 by Hairer, Martin, Mattingly, Jonathan · 4 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
11. Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling
    2001/09/18 by Martin Hairer, Hairer, Martin · 2 citations
    Mathematics · Physics and Astronomy · #60H15 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60H15
12. Hörmander's theorem for semilinear SPDEs
    2018/11/15 by Gerasimovics, Andris, Hairer, Martin · 3 citations
    #60H05 #60H07 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
13. A central limit theorem for the KPZ equation
    2015/07/05 by Hairer, Martin, Shen, Hao · 2 citations
    #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
14. An analyst's take on the BPHZ theorem
    2017/04/27 by Hairer, Martin · 2 citations
    #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
15. Large-scale limit of interface fluctuation models
    2018/02/22 by Martin Hairer, Hairer, Martin, Weijun Xu +1 · 2 citations
    Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
16. Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion
    2003/04/10 by Martin Hairer, Hairer, Martin · 1 citation
    Mathematics · #37H10 #60G10 #60H10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:37H10 #msc:60G10 #msc:60H10
17. Renormalisation in the presence of variance blowup
    2024/01/19 by Hairer, Martin · 3 citations
    #60H10 #60H15 #60L20 #60L30 #FOS: Mathematics #Probability (math.PR)
18. Periodic homogenization with an interface: the one-dimensional case
    2009/02/19 by Hairer, Martin, Manson, Charles · 1 citation
    #35B27 #60H10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
19. Periodic homogenization with an interface
    2009/10/02 by Hairer, Martin, Manson, Charles · 1 citation
    #FOS: Mathematics #Probability (math.PR)
20. Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
    2009/09/24 by Martin Hairer, Hairer, Martin, Natesh S. Pillai +1 · 1 citation
    Economics, Econometrics and Finance · Mathematics · #26A33 #60G10 #60H07 #60H10 #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications
21. A noise-induced transition in the Lorenz system
    2020/04/27 by Zelati, Michele Coti, Hairer, Martin · 2 citations
    #37H20 #60H10 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
22. A chain of interacting particles under strain
    2010/07/18 by Allman, Michael, Betz, Volker, Hairer, Martin · 1 citation
    #34E15 #60H10 #60J70 #FOS: Mathematics #Probability (math.PR)
23. Non-asymptotic mixing of the MALA algorithm
    2010/08/20 by Bou-Rabee, Nawaf, Hairer, Martin, Vanden-Eijnden, Eric · 1 citation
    #60J05 (Primary) 65C30 #65C05 (Secondary) #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Statistics Theory (math.ST)
24. Rough Stochastic PDEs
    2010/08/10 by Hairer, Martin · 1 citation
    #35R25 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
25. On Malliavin's proof of Hörmander's theorem
    2011/03/10 by Martin Hairer, Hairer, Martin · 1 citation
    Mathematics · #35H10 #60H07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Probability (math.PR) #advanced mathematical theories
26. Introduction to Regularity Structures
    2014/01/13 by Martin Hairer, Hairer, Martin · 1 citation
    Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Probability (math.PR) #Stochastic processes and financial applications
27. A fractional kinetic process describing the intermediate time behaviour of cellular flows
    2016/07/07 by Hairer, Martin, Iyer, Gautam, Koralov, Leonid +2 · 1 citation
    #26A33 #35R11 #60F17 #60H10 #60H30 #76R50 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
28. Tightness of the Ising-Kac model on the two-dimensional torus
    2017/12/22 by Hairer, Martin, Iberti, Massimo · 1 citation
    #60K35 #82C20 #82C22 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
29. The dynamical sine-Gordon model in the full subcritical regime
    2018/08/08 by Chandra, Ajay, Hairer, Martin, Shen, Hao · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
30. Singularity of solutions to singular SPDEs
    2024/09/16 by Hairer, Martin, Kusuoka, Seiichiro, Nagoji, Hirotatsu · 3 citations
    #60H15 #60H17 #FOS: Mathematics #Probability (math.PR)
31. Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization
    2016/02/12 by Charles-Édouard Bréhier, Bréhier, Charles-Edouard, Martin Hairer +3 · 2 citations
    Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications
32. A scaling limit of the parabolic Anderson model with exclusion interaction
    2021/03/24 by Dirk Erhard, Martin Hairer, Erhard, Dirk +1 · 1 citation
    Mathematics · Physics and Astronomy · #60H15 #60K35 #60L30 #60L90 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
33. Fluctuations of stochastic PDEs with long-range correlations
    2023/03/17 by Luca Gerolla, Gerolla, Luca, Martin Hairer +3 · 2 citations
    Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and financial applications
34. The Allen-Cahn equation with generic initial datum
    2022/01/20 by Hairer, Martin, Lê, Khoa, Rosati, Tommaso · 1 citation
    #35R60 #53E10 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
35. Lower bounds on the top Lyapunov exponent for linear PDEs driven by the 2D stochastic Navier-Stokes equations
    2024/11/15 by Hairer, Martin, Punshon-Smith, Sam, Rosati, Tommaso +1 · 2 citations
    #35Q35 #37H15 #37L30 #60H15 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
36. Scaling limit of the KPZ equation with non-integrable spatial correlations
    2024/07/18 by Gerolla, Luca, Hairer, Martin, Li, Xue-Mei · 2 citations
    #60F17 #60H15 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
37. Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise
    2023/01/26 by Hairer, Martin, Rosati, Tommaso · 1 citation
    #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
38. The support of singular stochastic PDEs
    2019/09/12 by Martin Hairer, Hairer, Martin, Philipp Schönbauer +1 · 3 citations
    Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods
39. A simple construction of the sine-Gordon model via stochastic quantization
    2024/12/20 by Gubinelli, Massimiliano, Hairer, Martin, Oh, Tadahiro +1 · 1 citation
    #35K05 #35L71 #60H15 #81T08 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
40. Regularity Structures on Manifolds and Vector Bundles
    2023/08/09 by Hairer, Martin, Singh, Harprit · 1 citation
    #60H15 #60L30 #FOS: Mathematics #Probability (math.PR)
41. Uniqueness of supercritical Gaussian multiplicative chaos
    2025/04/10 by Federico Bertacco, Martin Hairer, Bertacco, Federico +1 · 1 citation
    Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
42. A scaling limit of the 2D parabolic Anderson model with exclusion interaction
    2024/03/26 by Dirk Erhard, Erhard, Dirk, Martin Hairer +3 · 1 citation
    Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics