# American Institute of Mathematical Sciences

June  2011, 6(2): 167-194. doi: 10.3934/nhm.2011.6.167

## A central limit theorem for pulled fronts in a random medium

 1 Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, United States

Received  August 2010 Revised  February 2011 Published  May 2011

We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is the KPP type nonlinearity. For a stationary and ergodic medium, and for certain initial condition, the solution develops a moving front that has a deterministic asymptotic speed in the large time limit. The main result of this article is a central limit theorem for the position of the front, in the supercritical regime, if the medium satisfies a mixing condition.
Citation: James Nolen. A central limit theorem for pulled fronts in a random medium. Networks & Heterogeneous Media, 2011, 6 (2) : 167-194. doi: 10.3934/nhm.2011.6.167
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