# 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

##### 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)

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, 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.
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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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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).
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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.": Springer Berlin Heidelberg, 2012. Full Text