Preprints

  1. S. Armstrong and T. Kuusi. Renormalization group and elliptic homogenization in high contrast. arXiv | blog post
  2. S. Armstrong, A. Bou-Rabee and T. Kuusi. Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift. arXiv | blog post | youtube
  3. S. Armstrong and W. Wu. The scaling limit of the continuous solid-on-solid model. arXiv
  4. S. Armstrong and R. Venkatraman. Quantitative homogenization and large-scale regularity of Poisson point clouds. arXiv
  5. S. Armstrong, B. Fehrman and J. Lin. Green function and invariant measure estimates for nondivergence form
      elliptic homogenization. arXiv
  6. S. Armstrong, T. Kuusi and C. Smart. Optimal unique continuation for periodic elliptic equations on large scales. arXiv

Books/Monographs

  1. S. Armstrong and T. Kuusi. Elliptic Homogenization from Qualitative to Quantitative. arXiv | blog post | github
  2. S. Armstrong, T. Kuusi and J.-C. Mourrat. Quantitative Stochastic Homogenization and Large-Scale Regularity. Grundlehren der mathematischen Wissenschaften vol. 352, Springer-Nature, Cham, 2019. full text

Published Articles

  1. S. Armstrong and R. Venkatraman. Optimal convergence rates for the spectrum of the graph Laplacian on Poisson point clouds. Found. Comput. Math., in press. arXiv
  2. S. Armstrong and V. Vicol. Anomalous diffusion by fractal homogenization. Ann. PDE, 11 (2025) art. 2, 145p. arXiv | journal | blog post | youtube
  3. S. Armstrong and P. Dario. Quantitative hydrodynamic limits of the Langevin dynamics for gradient interface models. Electron. J. Probab., 29 (2024) 1-93. arXiv | journal
  4. S. Armstrong and R. Venkatraman. Asymptotic expansion of the spectrum for periodic Schrödinger operators. SIAM J. Math. Anal., 56 (2024) 1770-1808. arXiv | journal
  5. S. Armstrong, T. Kuusi and C. Smart. Large-scale analyticity and unique continuation for periodic elliptic equations. Comm. Pure Appl. Math., 76 (2023), 73-113. arXiv | journal
  6. S. Armstrong and S. Serfaty. Thermal approximation of the equilibrium measure and obstacle problem. Ann. Fac. Sci. Toulouse Math., 31 (2022) no. 4, pp. 1085-1110. arXiv | journal
  7. S. Armstrong, S. Ferguson and T. Kuusi. Higher-order linearization and regularity in nonlinear homogenization. Arch. Ration. Mech. Anal., 237 (2020), 631-741. arXiv | journal
  8. S. Armstrong and W. Wu. C^2 regularity of the surface tension for the \nabla\phi interface model. Comm. Pure Appl. Math., 75 (2022), 349-421. arXiv | journal 
  9. S. Armstrong and S. Serfaty. Local laws and rigidity for Coulomb gases at any temperature. Ann. Probab., 49 (2021) 46-121. arXiv | journal
  10. D. Albritton, S. Armstrong, J.-C. Mourrat and M. Novack. Variational methods for the kinetic Fokker-Planck equation. Anal. & PDE, 17 (2024), 1953-2010. arXiv | journal
  11. S. Armstrong, S. Ferguson and T. Kuusi. Homogenization, linearization and large-scale regularity for nonlinear elliptic equations. Comm. Pure Appl. Math., 74 (2021), 286-365. arXiv | journal
  12. S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat. An iterative method for elliptic problems with rapidly oscillating coefficients. ESAIM Math. Model. Numer. Anal. 55 (2021), 37-55. arXiv | journal
  13. S. Armstrong, A. Bordas and J.-C. Mourrat. Quantitative stochastic homogenization and regularity theory of parabolic equations. Anal. & PDE, 11 (2018), 1945-2014. arXiv | journal
  14. S. Armstrong and P. Dario. Elliptic regularity and quantitative homogenization on percolation clusters. Comm. Pure Appl. Math., 71 (2018), 1717-1849. arXiv | journal
  15. S. Armstrong, T. Kuusi, J.-C. Mourrat and C. Prange. Quantitative analysis of boundary layers in periodic homogenization. Arch. Ration. Mech. Anal., 226 (2017), 695-741. arXiv | journal
  16. S. Armstrong and J. Lin. Optimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form. Arch. Ration. Mech. Anal., 225 (2017), 937-991. arXiv | journal
  17. S. Armstrong, T. Kuusi and J.-C. Mourrat. The additive structure of elliptic homogenization. Invent. Math., 208 (2017), 999-1154. arXiv | journal
  18. S. Armstrong, A. Gloria and T. Kuusi. Bounded correctors in almost periodic homogenization. Arch. Ration. Mech. Anal., 222 (2016), 393-426. arXiv | journal
  19. S. Armstrong, T. Kuusi and J.-C. Mourrat. Mesoscopic higher regularity and subadditivity in elliptic homogenization. Comm. Math. Phys., 347 (2016), 315-361. arXiv | journal
  20. S. Armstrong and J.-P. Daniel. Calderón-Zygmund estimates for stochastic homogenization. J. Functional Anal., 270 (2016), 312-329. arXiv | journal
  21. S. Armstrong and P. Cardaliaguet. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc., 20 (2018), 797-864. arXiv | journal
  22. S. N. Armstrong and J.-C. Mourrat. Lipschitz regularity for elliptic equations with random coefficients. Arch. Ration. Mech. Anal., 219 (2016), 255-348. arXiv | journal
  23. S. N. Armstrong, H. V. Tran and Y. Yu. Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension. J. Differential Equations, 261 (2016), 2702-2737. arXiv | journal
  24. S. N. Armstrong and Z. Shen. Lipschitz estimates in almost-periodic homogenization. Comm. Pure Appl. Math., 69 (2016), 1882-1923. arXiv | journal
  25. S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of convex integral functionals. Ann. Sci. Éc. Norm. Supér., 48 (2016), 423-481. arXiv | journal. This paper received the 2017 SIAG/APDE Prize for most outstanding paper in PDE.
  26. S. N. Armstrong and O. Zeitouni. Local asymptotics for controlled martingales. Ann. Appl. Probab., 26 (2016), 1467-1494. arXiv | journal
  27. S. N. Armstrong, H. V. Tran and Y. Yu. Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Calc. Var. Partial Differential Equations, 54 (2015), 1507-1524. arXiv | journal
  28. S. N. Armstrong and P. Cardaliaguet. Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations, Comm. PDE, 40 (2015), 540-600. arXiv | journal
  29. S. N. Armstrong and H. V. Tran. Stochastic homogenization of viscous Hamilton-Jacobi equations and applications, Anal. & PDE, 7-8 (2014), 1969-2007. arXiv | journal
  30. S. N. Armstrong and H. V. Tran. Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann., 361 (2015), 647-687. arXiv | journal
  31. S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of elliptic equations in nondivergence form, Arch. Ration. Mech. Anal., 214 (2014), 867-911. arXiv | journal
  32. S. N. Armstrong, S. Serfaty and O. Zeitouni. Remarks on a constrained optimization problem for the Ginibre ensemble, Potential Anal. 41 (2014), 945-958. arXiv | journal
  33. S. N. Armstrong and C. K. Smart. Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited, Calc. Var. Partial Differential Equations 50 (2014), 967-980. arXiv | journal
  34. S. N. Armstrong and C. K. Smart. Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity, Ann. Probab., 42 (2014), 2558-2594. arXiv | journal
  35. S. N. Armstrong, P. Cardaliaguet and P. E. Souganidis. Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations, J. Amer. Math. Soc., 27 (2014), 479-540. arXiv | journal
  36. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of level-set convex Hamilton-Jacobi equations, Int. Math. Res. Not., 2013 (2013), 3420-3449. arXiv | journal
  37. S. N. Armstrong and P. E. Souganidis. Concentration phenomena for neutronic multigroup diffusion in random environments, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 419-439. arXiv | journal
  38. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of L^\infty variational problems, Adv. Math., 229 (2012), no. 6, 3508-3535. arXiv | journal
  39. S. N. Armstrong, B. Sirakov and C. K. Smart. Singular solutions of fully nonlinear elliptic equations and applications, Arch. Ration. Mech. Anal., 205 (2012), no. 2, 345-394. arXiv | journal
  40. S. N. Armstrong, L. Silvestre and C. K. Smart. Partial regularity of solutions of fully nonlinear uniformly elliptic equations, Comm. Pure Appl. Math., 65 (2012), no. 8, 1169-1184. arXiv | journal
  41. S. N. Armstrong and P. E. Souganidis. Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments, J. Math. Pures Appl. (9), 97 (2012), no. 5, 460-504. arXiv | journal
  42. S. N. Armstrong and L. Silvestre. Unique continuation for fully nonlinear elliptic equations, Math. Res. Lett., 18 (2011), no. 5, 921-926. arXiv | journal
  43. S. N. Armstrong and B. Sirakov. Nonexistence of positive supersolutions of elliptic equations via the maximum principle, Comm. PDE, 36 (2011), no. 11, 2011-2047. arXiv | journal
  44. S. N. Armstrong, M. G. Crandall, V. Julin, and C. K. Smart. Convexity criteria and uniqueness of absolutely minimizing functions, Arch. Ration. Mech. Anal., 200 (2011), no. 2, 405-443. arXiv | journal
  45. S. N. Armstrong and B. Sirakov. Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 10 (2011), no. 3, 711-728. arXiv | journal
  46. S. N. Armstrong, B. Sirakov and C. K. Smart. Fundamental solutions of homogeneous fully nonlinear elliptic equations, Comm. Pure Appl. Math., 64 (2011), no. 6, 737-777. arXiv | journal
  47. S. N. Armstrong, C. K. Smart and S. J. Somersille. An infinity Laplace equation with gradient term and mixed boundary conditions, Proc. Amer. Math. Soc., 139 (2011), no. 5, 1763-1776. arXiv | journal
  48. S. N. Armstrong and C. K. Smart. An easy proof of Jensen’s theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations 37 (2010), 381-384. arXiv | journal
  49. S. N. Armstrong and C. K. Smart. A finite difference approach to the infinity Laplace equation and tug-of-war games, Trans. Amer. Math. Soc. 364 (2012), no. 2, 595-636. arXiv | journal
  50. S. N. Armstrong and M. Trokhimtchouk. Long-time asymptotics for fully nonlinear homogeneous parabolic equations, Calc. Var. Partial Differential Equations 38 (2010), 521-540. arXiv | journal
  51. S. N. Armstrong. The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations 247 (2009), 931-955. arXiv| journal
  52. S. N. Armstrong. Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations, J. Differential Equations 246 (2009), 2958-2987. arXiv | journal
  53. S. N. Armstrong and C. J. Hillar. Solvability of symmetric word equations in positive definite letters, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 777-796. arxiv | journal
  54. S. Armstrong, K. Dykema, R. Exel and H. Li. On embeddings of full amalgamated free product C*-algebras, Proc. Amer. Math. Soc. 132 (2004), no. 7, 2019-2030. arxiv | journal