Stability and Convergence of the String Method for Computing Minimum Energy Paths

We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.