James H. Nolen

James H. Nolen
  • Associate Professor of Mathematics
External address: 243 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2862
Office Hours: 

Mondays 2:30-4:00
Wednesdays, 10:30-12:00

Research Areas and Keywords

partial differential equations, probability, asymptotic analysis, homogenization
Biological Modeling
asymptotic analysis
PDE & Dynamical Systems
reactive diffusion equations & applications, homogenization of partial differential equations, random media, asymptotic analysis
Physical Modeling
asymptotic analysis
homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

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.

Education & Training
  • Ph.D., University of Texas at Austin 2006

  • B.S., Davidson College 2000

Selected Grants

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

Fellowships, Supported Research, & Other Grants

NSF Postdoctoral Research Fellowship awarded by National Science Foundation (2006 to 2008)

Cristali, I, Ranjan, V, Steinberg, J, Beckman, E, Durrett, R, Junge, M, and Nolen, J. "Block size in geometric(P)-biased permutations." Electronic Communications in Probability 23 (January 1, 2018). Full Text

Mourrat, JC, and Nolen, J. "Scaling limit of the corrector in stochastic homogenization." Annals of Applied Probability 27.2 (April 1, 2017): 944-959. Full Text

Nolen, J, Roquejoffre, JM, and Ryzhik, L. "Convergence to a single wave in the Fisher-KPP equation." Chinese Annals of Mathematics. Series B 38.2 (March 1, 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 1, 2016): 2304-2348. Full Text

Hamel, F, Nolen, J, Roquejoffre, JM, and Ryzhik, L. "The logarithmic delay of KPP fronts in a periodic medium." Journal of the European Mathematical Society 18.3 (January 1, 2016): 465-505. Full Text

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 (October 19, 2015). 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, JC, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electronic Journal of Probability 20 (January 1, 2015). Full Text Open Access Copy

Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields 159.3-4 (2014): 661-700. Full Text


Nolen, J, Pavliotis, GA, and Stuart, AM. "Multiscale Modelling and Inverse Problems.": Springer Berlin Heidelberg, 2012. Full Text