# 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, 1-2:30

Wednesdays, 10:30-12

### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

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

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.
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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.
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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.
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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.
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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.
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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.
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Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." *Probability Theory and Related Fields* 161.1-2 (February 2015): 195-244.
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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).
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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).
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