Scott Armstrong

About

Professor Scott Armstrong is a faculty member in the Department of Mathematics at NYU. His research interests include partial differential equations, probability theory, and stochastic homogenization. As a professor, he contributes to the mathematical community through his focus on these areas, advancing understanding in the behavior of complex systems described by PDEs and probabilistic models.

Research topics

• Mathematics
• Applied mathematics
• Mathematical analysis
• Physics

Selected publications

• Quantitative Stochastic Homogenization and Large-Scale Regularity

  Grundlehren der mathematischen Wissenschaften · 2019-01-01 · 180 citations

  bookOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Variational methods for the kineticFokker–Planck equation

  Analysis & PDE · 2024-07-19 · 15 citations

  articleOpen access

  We develop a functional-analytic approach to the study of the Kramers and kinetic Fokker-Planck equations which parallels the classical H 1 theory of uniformly elliptic equations.In particular, we identify a function space analogous to H 1 and develop a well-posedness theory for weak solutions in this space.In the case of a conservative force, we identify the weak solution as the minimizer of a uniformly convex functional.We prove new functional inequalities of Poincar-and Hrmander-type and comb…

  PublisherOA PDFDOI

• Thermal approximation of the equilibrium measure and obstacle problem

  Annales de la faculté des sciences de Toulouse Mathématiques · 2022-10-28 · 12 citations

  articleOpen access1st authorCorresponding

  We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where the inverse temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> tends to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> the entropy term disappears and the measure, which…

  PublisherOA PDFDOI

• Homogenization, Linearization, and <scp>Large‐Scale</scp> Regularity for Nonlinear Elliptic Equations

  Communications on Pure and Applied Mathematics · 2020 · 11 citations

  1st authorCorresponding

  Abstract We consider nonlinear, uniformly elliptic equations with random, highly oscillating coefficients satisfying a finite range of dependence. We prove that homogenization and linearization commute in the sense that the linearized equation (linearized around an arbitrary solution) homogenizes to the linearization of the homogenized equation (linearized around the corresponding solution of the homogenized equation). We also obtain a quantitative estimate on the rate of this homogenization. Th…

  PublisherDOI

• <scp>Large‐Scale</scp> Analyticity and Unique Continuation for Periodic Elliptic Equations

  Communications on Pure and Applied Mathematics · 2020-10-27 · 11 citations

  article1st authorCorresponding

  Abstract We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the large‐scale C k , 1 estimate scale exponentially in k , just as for the classical estimate for harmonic functions, and the minimal scale grows at most linearly in k . As a consequence, we characterize entire solutions of periodic, uniformly elliptic equation…

  PublisherDOI

Recent grants

• PostDoctoral Research Fellowship

  NSF · $135k · 2010–2014

Frequent coauthors

• Guofang Tokyo

  Walter de Gruyter (Germany)

  75 shared

• Parma Mingione

  Walter de Gruyter (Germany)

  75 shared

• Tristan Uppsala

  Friedrich-Alexander-Universität Erlangen-Nürnberg

  75 shared

• Luis Shen

  Friedrich-Alexander-Universität Erlangen-Nürnberg

  75 shared

• Giuseppe Martell

  Walter de Gruyter (Germany)

  75 shared

• Pavia Gianazza

  Friedrich-Alexander-Universität Erlangen-Nürnberg

  75 shared

• Bernard Dacorogna

  École Polytechnique Fédérale de Lausanne

  75 shared

• Yoshihiro Chicago

  Walter de Gruyter (Germany)

  75 shared

Education

• Ph.D.

  University of California, Berkeley

  2009

• B.S.

  Texas A&M University

  2002

Similar researchers at New York University

• Fedor Bogomolovh-32
• Paul Bourgadeh-28
• Yuri Bakhtinh-18