| Abstract: |
| Locally isotropic Gaussian random fields were first introduced by Kolmogorov in 1941. Such models were used widely in statistical physics. In particular, they were introduced to model a single particle in a random potential by Engel, Mezard and Parisi in 1990s. Using Parisi`s award winning replica trick, Fyodorov and Le Doussal predicted the high dimensional limit of the Hessian spectrum at the global minimum of these models, and discovered phase transitions according to different levels of replica symmetry breaking. In this talk, I will present a solution in a strong sense to their conjecture in the so called replica symmetric regime. Our method is based on landscape complexity, or counting the number of critical points of the Hamiltonian. This talk is based on joint works with Antonio Auffinger (Northwestern University) and Hao Xu (University of Macau). |
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