Higher multiplicity in the one-dimensional Allen-Cahn action functional Yoshihiro TonegawaMaria Westdickenberg 49J4535R6060F10Allen-Cahn equationstochastic partial differntial equationslarge deviation theoryaction minimizationsharp-interface limits$\gamma$-convergence We prove the $\Gamma$-convergence of the one-dimensional Allen-Cahn action functional in the sharp-interface limit. In previous work, a good lower bound was developed under the assumption of single multiplicity, but the bound deteriorated in the case of higher multiplicity interfaces. We develop an improved bound by working directly with the limiting energy measures. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3182 10.1512/iumj.2007.56.3182 en Indiana Univ. Math. J. 56 (2007) 2935 - 2990 state-of-the-art mathematics http://iumj.org/access/