# 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, 10:30-12:00

Wednesdays, 2:00-3:30

### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

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.

### 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)

Nolen, J, Roquejoffre, JM, and Ryzhik, L. "Refined long-time asymptotics for Fisher-KPP fronts(Accepted)." *Communications in Contemporary Mathematics* (January 1, 2018).
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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).
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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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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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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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## Pages

Nolen, J, Pavliotis, GA, and Stuart, AM. "Multiscale modelling and inverse problems." January 1, 2012. Full Text