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Abstract |
We show that for a large class of random Lagrangian systems the unique global minimizer is almost surely hyperbolic. Furthermore, we prove that the unique forward and backward viscosity solutions for the corresponding Hasmilton-Jacobi equation, though in general only Lipshitz, are smooth in a neighborhood of the global minimizer. Related results in the one-dimensional case were obtained by E, Khanin, Mazel and Sinai (Annals, 2000). However the methods of the above paper cannot be extended to the case of higher dimensions. In this talk based on a joint paper with Ke Zhang we present a different approach to the problem of hyperbolicity. |
