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Many complex disordered systems in statistical mechanics are characterized by intricate energy landscapes.

The ground state, the configuration with the lowest energy, lies at the base of the deepest valley. In important examples, such as Gaussian polymers and spin glass models, the landscape has many valleys and the abundance of near-ground states (at the base of the valleys) indicates the phenomenon of chaos, under which the ground state alters profoundly when the disorder of the model is slightly perturbed.

In this talk, we will discuss work with Alan Hammond computing the critical exponent that governs the onset of chaos in a dynamic manifestation of a canonical planar last passage percolation model in the Kardar-Parisi-Zhang universality class. We expect this exponent to be universal across a wide range of interface and stochastic growth models. The arguments rely on Chatterjee's harmonic analytic theory of equivalence of super-concentration and chaos in Gaussian spaces and a refined understanding of the corresponding static landscape geometry.