We give an analysis of the stability and convergence of the improved string method of E, Ren, and Vanden-Eijnden to a minimum energy path. In the simplest setting of an index one saddle point connecting two linearly stable local minimum, we show that the string method initialized in a neighborhood of a minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

Joint work with Mitchell Luskin