- Associate Professor of Mathematics
I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic analysis has been a common theme in much of my research. Current research interests include: reaction diffusion equations, homogenization of PDEs, stochastic dynamics, interacting particle systems.
Ph.D., University of Texas at Austin 2006
B.S., Davidson College 2000
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
Mourrat, J-C, and Nolen, J. "Scaling limit of the corrector in stochastic homogenization." The Annals of Applied Probability 27.2 (April 2017): 944-959. Full Text
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, 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 Open Access Copy
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