James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability. I also study the asymptotic behavior of stochastic processes.
CAREER: Research and training in stochastic dynamics awarded by National Science Foundation (Principal Investigator). 2014 to 2019
Analysis of Fluctuations awarded by National Science Foundation (Principal Investigator). 2010 to 2015
Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "Convergence to a single wave in the Fisher-KPP equation." Chinese Annals of Mathematics, Series B 38.2 (March 2017): 629-646. Full Text
Gloria, A, and Nolen, J. "A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus." Communications on Pure and Applied Mathematics 69.12 (December 2016): 2304-2348. Full Text
Nolen, J. "Normal approximation for the net flux through a random conductor." Stochastics and Partial Differential Equations: Analysis and Computations 4.3 (September 2016): 439-476. Full Text
Nolen, J, and Mourrat, J-C. "Scaling limit of the corrector in stochastic homogenization (Accepted)." Annals of Applied Probability (2016).
Nolen, JH, Roquejoffre, J-M, and Ryzhik, L. "Refined long time asymptotics for Fisher-KPP fronts (Submitted)." (2016).
Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "The logarithmic delay of KPP fronts in a periodic medium." Journal of the European Mathematical Society 18.3 (2016): 465-505. Full Text
Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "Power-Like Delay in Time Inhomogeneous Fisher-KPP Equations." Communications in Partial Differential Equations 40.3 (March 4, 2015): 475-505. Full Text
Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." Probability Theory and Related Fields 161.1-2 (February 2015): 195-244. Full Text
Huckemann, S, Mattingly, J, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electronic Journal of Probability 20.0 (2015). Full Text Open Access Copy
Bhamidi, S, Hannig, J, Lee, CY, and Nolen, J. "The importance sampling technique for understanding rare events in Erdős–Rényi random graphs." Electronic Journal of Probability 20.0 (2015). Full Text