Abstract
We prove the hyperbolicity of global minimizers for random Lagrangian systems in dimension 1. The proof considerably simplifies a related result in Weinan E et al (2000 Ann. Math. 151 877–960). The conditions for hyperbolicity are almost optimal: they are essentially the same as the conditions for uniqueness of a global minimizer in Iturriaga and Khanin (2003 Commun. Math. Phys. 232 377–428).
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