On hyperbolicity of minimizers for 1D random Lagrangian systems
Alexandre Boritchev, Konstantin Khanin
TL;DR
This paper proves the hyperbolicity of global minimizers in one-dimensional random Lagrangian systems, simplifying previous proofs and establishing near-optimal conditions for hyperbolicity that align with conditions for uniqueness.
Contribution
It provides a simplified proof of hyperbolicity for global minimizers and identifies near-optimal conditions that match those for their uniqueness.
Findings
Hyperbolicity of global minimizers is established.
Conditions for hyperbolicity are nearly optimal.
Simplification of previous related proofs.
Abstract
We prove hyperbolicity of global minimizers for random Lagrangian systems in dimension 1. The proof considerably simplifies a related result in [2]. The conditions for hyperbolicity are almost optimal: they are essentially the same as conditions for uniqueness of a global minimizer in [3].
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